Solve by Factoring square root of 4x+37=x+8

$\sqrt{4 x + 37} = x + 8$

Step 1

Move all the expressions to the left side of the equation.

Subtract $x$ from both sides of the equation.

$\sqrt{4 x + 37} - x = 8$

Subtract $8$ from both sides of the equation.

$\sqrt{4 x + 37} - x - 8 = 0$

Step 2

Move all terms not containing $\sqrt{4 x + 37}$ to the right side of the equation.

Add $x$ to both sides of the equation.

$\sqrt{4 x + 37} - 8 = x$

Add $8$ to both sides of the equation.

$\sqrt{4 x + 37} = x + 8$

Step 3

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

${\sqrt{4 x + 37}}^{2} = {(x + 8)}^{2}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 x + 37}$ as ${(4 x + 37)}^{\frac{1}{2}}$ .

${({(4 x + 37)}^{\frac{1}{2}})}^{2} = {(x + 8)}^{2}$

Simplify the left side.

Simplify ${({(4 x + 37)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(4 x + 37)}^{\frac{1}{2}})}^{2}$ .

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

${(4 x + 37)}^{\frac{1}{2} \cdot 2} = {(x + 8)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 x + 37)}^{\frac{1}{2} \cdot 2} = {(x + 8)}^{2}$

Rewrite the expression.

${(4 x + 37)}^{1} = {(x + 8)}^{2}$

Simplify.

$4 x + 37 = {(x + 8)}^{2}$

Simplify the right side.

Simplify ${(x + 8)}^{2}$ .

Rewrite ${(x + 8)}^{2}$ as $(x + 8) (x + 8)$ .

$4 x + 37 = (x + 8) (x + 8)$

Expand $(x + 8) (x + 8)$ using the FOIL Method.

Apply the distributive property.

$4 x + 37 = x (x + 8) + 8 (x + 8)$

Apply the distributive property.

$4 x + 37 = x \cdot x + x \cdot 8 + 8 (x + 8)$

Apply the distributive property.

$4 x + 37 = x \cdot x + x \cdot 8 + 8 x + 8 \cdot 8$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$4 x + 37 = x^{2} + x \cdot 8 + 8 x + 8 \cdot 8$

Move $8$ to the left of $x$ .

$4 x + 37 = x^{2} + 8 \cdot x + 8 x + 8 \cdot 8$

Multiply $8$ by $8$ .

$4 x + 37 = x^{2} + 8 x + 8 x + 64$

Add $8 x$ and $8 x$ .

$4 x + 37 = x^{2} + 16 x + 64$

Step 5

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.

$x^{2} + 16 x + 64 = 4 x + 37$

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

Subtract $4 x$ from both sides of the equation.

$x^{2} + 16 x + 64 - 4 x = 37$

Subtract $4 x$ from $16 x$ .

$x^{2} + 12 x + 64 = 37$

Subtract $37$ from both sides of the equation.

$x^{2} + 12 x + 64 - 37 = 0$

Subtract $37$ from $64$ .

$x^{2} + 12 x + 27 = 0$

Factor $x^{2} + 12 x + 27$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $27$ and whose sum is $12$ .

$3, 9$

Write the factored form using these integers.

$(x + 3) (x + 9) = 0$

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

$x + 3 = 0$

$x + 9 = 0$

Set $x + 3$ equal to $0$ and solve for $x$ .

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Set $x + 9$ equal to $0$ and solve for $x$ .

Set $x + 9$ equal to $0$ .

$x + 9 = 0$

Subtract $9$ from both sides of the equation.

$x = - 9$

The final solution is all the values that make $(x + 3) (x + 9) = 0$ true.

$x = - 3, - 9$

Step 6

Exclude the solutions that do not make $\sqrt{4 x + 37} - x - 8 = 0$ true.

$x = - 3$

Solve by Factoring square root of 4x+37=x+8

Related Questions

Support LCMGCF.com by disabling your adblocker.