Solve for x square root of 8x+4=2x+1

$\sqrt{8 x + 4} = 2 x + 1$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{8 x + 4}}^{2} = {(2 x + 1)}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{8 x + 4}$ as ${(8 x + 4)}^{\frac{1}{2}}$ .

${({(8 x + 4)}^{\frac{1}{2}})}^{2} = {(2 x + 1)}^{2}$

Simplify the left side.

Simplify ${({(8 x + 4)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(8 x + 4)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(8 x + 4)}^{\frac{1}{2} \cdot 2} = {(2 x + 1)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(8 x + 4)}^{\frac{1}{2} \cdot 2} = {(2 x + 1)}^{2}$

Rewrite the expression.

${(8 x + 4)}^{1} = {(2 x + 1)}^{2}$

Simplify.

$8 x + 4 = {(2 x + 1)}^{2}$

Simplify the right side.

Simplify ${(2 x + 1)}^{2}$ .

Rewrite ${(2 x + 1)}^{2}$ as $(2 x + 1) (2 x + 1)$ .

$8 x + 4 = (2 x + 1) (2 x + 1)$

Expand $(2 x + 1) (2 x + 1)$ using the FOIL Method.

Apply the distributive property.

$8 x + 4 = 2 x (2 x + 1) + 1 (2 x + 1)$

Apply the distributive property.

$8 x + 4 = 2 x (2 x) + 2 x \cdot 1 + 1 (2 x + 1)$

Apply the distributive property.

$8 x + 4 = 2 x (2 x) + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$8 x + 4 = 2 \cdot 2 x \cdot x + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$8 x + 4 = 2 \cdot 2 (x \cdot x) + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1$

Multiply $x$ by $x$ .

$8 x + 4 = 2 \cdot 2 x^{2} + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1$

Multiply $2$ by $2$ .

$8 x + 4 = 4 x^{2} + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1$

Multiply $2$ by $1$ .

$8 x + 4 = 4 x^{2} + 2 x + 1 (2 x) + 1 \cdot 1$

Multiply $2 x$ by $1$ .

$8 x + 4 = 4 x^{2} + 2 x + 2 x + 1 \cdot 1$

Multiply $1$ by $1$ .

$8 x + 4 = 4 x^{2} + 2 x + 2 x + 1$

Add $2 x$ and $2 x$ .

$8 x + 4 = 4 x^{2} + 4 x + 1$

Solve for $x$ .

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$4 x^{2} + 4 x + 1 = 8 x + 4$

Move all terms containing $x$ to the left side of the equation.

Subtract $8 x$ from both sides of the equation.

$4 x^{2} + 4 x + 1 - 8 x = 4$

Subtract $8 x$ from $4 x$ .

$4 x^{2} - 4 x + 1 = 4$

Subtract $4$ from both sides of the equation.

$4 x^{2} - 4 x + 1 - 4 = 0$

Subtract $4$ from $1$ .

$4 x^{2} - 4 x - 3 = 0$

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 4 \cdot - 3 = - 12$ and whose sum is $b = - 4$ .

Factor $- 4$ out of $- 4 x$ .

$4 x^{2} - 4 x - 3 = 0$

Rewrite $- 4$ as $2$ plus $- 6$

$4 x^{2} + (2 - 6) x - 3 = 0$

Apply the distributive property.

$4 x^{2} + 2 x - 6 x - 3 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} + 2 x) - 6 x - 3 = 0$

Factor out the greatest common factor (GCF) from each group.

$2 x (2 x + 1) - 3 (2 x + 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

$(2 x + 1) (2 x - 3) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$2 x + 1 = 0$

$2 x - 3 = 0$

Set $2 x + 1$ equal to $0$ and solve for $x$ .

Set $2 x + 1$ equal to $0$ .

$2 x + 1 = 0$

Solve $2 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$2 x = - 1$

Divide each term in $2 x = - 1$ by $2$ and simplify.

Divide each term in $2 x = - 1$ by $2$ .

$\frac{2 x}{2} = \frac{- 1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 1}{2}$

Divide $x$ by $1$ .

$x = \frac{- 1}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

Set $2 x - 3$ equal to $0$ and solve for $x$ .

Set $2 x - 3$ equal to $0$ .

$2 x - 3 = 0$

Solve $2 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$2 x = 3$

Divide each term in $2 x = 3$ by $2$ and simplify.

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Divide $x$ by $1$ .

$x = \frac{3}{2}$

The final solution is all the values that make $(2 x + 1) (2 x - 3) = 0$ true.

$x = - \frac{1}{2}, \frac{3}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{2}, \frac{3}{2}$

Decimal Form:

$x = - 0.5, 1.5$

Mixed Number Form:

$x = - \frac{1}{2}, 1 \frac{1}{2}$

Solve for x square root of 8x+4=2x+1

Related Questions

Support LCMGCF.com by disabling your adblocker.