Solve for x 2x-5 square root of x+2=0

$2 x - 5 \sqrt{x} + 2 = 0$

Move all terms not containing $- 5 \sqrt{x}$ to the right side of the equation.

Subtract $2 x$ from both sides of the equation.

$- 5 \sqrt{x} + 2 = - 2 x$

Subtract $2$ from both sides of the equation.

$- 5 \sqrt{x} = - 2 x - 2$

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

${(- 5 \sqrt{x})}^{2} = {(- 2 x - 2)}^{2}$

Simplify each side of the equation.

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

${(- 5 x^{\frac{1}{2}})}^{2} = {(- 2 x - 2)}^{2}$

Simplify the left side.

Simplify ${(- 5 x^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $- 5 x^{\frac{1}{2}}$ .

${(- 5)}^{2} {(x^{\frac{1}{2}})}^{2} = {(- 2 x - 2)}^{2}$

Raise $- 5$ to the power of $2$ .

$25 {(x^{\frac{1}{2}})}^{2} = {(- 2 x - 2)}^{2}$

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

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

$25 x^{\frac{1}{2} \cdot 2} = {(- 2 x - 2)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$25 x^{\frac{1}{2} \cdot 2} = {(- 2 x - 2)}^{2}$

Rewrite the expression.

$25 x^{1} = {(- 2 x - 2)}^{2}$

Simplify.

$25 x = {(- 2 x - 2)}^{2}$

Simplify the right side.

Simplify ${(- 2 x - 2)}^{2}$ .

Rewrite ${(- 2 x - 2)}^{2}$ as $(- 2 x - 2) (- 2 x - 2)$ .

$25 x = (- 2 x - 2) (- 2 x - 2)$

Expand $(- 2 x - 2) (- 2 x - 2)$ using the FOIL Method.

Apply the distributive property.

$25 x = - 2 x (- 2 x - 2) - 2 (- 2 x - 2)$

Apply the distributive property.

$25 x = - 2 x (- 2 x) - 2 x \cdot - 2 - 2 (- 2 x - 2)$

Apply the distributive property.

$25 x = - 2 x (- 2 x) - 2 x \cdot - 2 - 2 (- 2 x) - 2 \cdot - 2$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$25 x = - 2 \cdot - 2 x \cdot x - 2 x \cdot - 2 - 2 (- 2 x) - 2 \cdot - 2$

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

Move $x$ .

$25 x = - 2 \cdot - 2 (x \cdot x) - 2 x \cdot - 2 - 2 (- 2 x) - 2 \cdot - 2$

Multiply $x$ by $x$ .

$25 x = - 2 \cdot - 2 x^{2} - 2 x \cdot - 2 - 2 (- 2 x) - 2 \cdot - 2$

Multiply $- 2$ by $- 2$ .

$25 x = 4 x^{2} - 2 x \cdot - 2 - 2 (- 2 x) - 2 \cdot - 2$

Multiply $- 2$ by $- 2$ .

$25 x = 4 x^{2} + 4 x - 2 (- 2 x) - 2 \cdot - 2$

Multiply $- 2$ by $- 2$ .

$25 x = 4 x^{2} + 4 x + 4 x - 2 \cdot - 2$

Multiply $- 2$ by $- 2$ .

$25 x = 4 x^{2} + 4 x + 4 x + 4$

Add $4 x$ and $4 x$ .

$25 x = 4 x^{2} + 8 x + 4$

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.

$4 x^{2} + 8 x + 4 = 25 x$

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

Subtract $25 x$ from both sides of the equation.

$4 x^{2} + 8 x + 4 - 25 x = 0$

Subtract $25 x$ from $8 x$ .

$4 x^{2} - 17 x + 4 = 0$

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 $a \cdot c = 4 \cdot 4 = 16$ and whose sum is $b = - 17$ .

Factor $- 17$ out of $- 17 x$ .

$4 x^{2} - 17 x + 4 = 0$

Rewrite $- 17$ as $- 1$ plus $- 16$

$4 x^{2} + (- 1 - 16) x + 4 = 0$

Apply the distributive property.

$4 x^{2} - 1 x - 16 x + 4 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} - 1 x) - 16 x + 4 = 0$

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

$x (4 x - 1) - 4 (4 x - 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $4 x - 1$ .

$(4 x - 1) (x - 4) = 0$

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

$4 x - 1 = 0$

$x - 4 = 0$

Set $4 x - 1$ equal to $0$ and solve for $x$ .

Set $4 x - 1$ equal to $0$ .

$4 x - 1 = 0$

Solve $4 x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$4 x = 1$

Divide each term in $4 x = 1$ by $4$ and simplify.

Divide each term in $4 x = 1$ by $4$ .

$\frac{4 x}{4} = \frac{1}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{1}{4}$

Divide $x$ by $1$ .

$x = \frac{1}{4}$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

The final solution is all the values that make $(4 x - 1) (x - 4) = 0$ true.

$x = \frac{1}{4}, 4$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{4}, 4$

Decimal Form:

$x = 0.25, 4$

Solve for x 2x-5 square root of x+2=0

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