Solve for X square root of 4X^2-12X+9=5

$\sqrt{4 X^{2} - 12 X + 9} = 5$

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

${\sqrt{4 X^{2} - 12 X + 9}}^{2} = 5^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 X^{2} - 12 X + 9}$ as ${(4 X^{2} - 12 X + 9)}^{\frac{1}{2}}$ .

${({(4 X^{2} - 12 X + 9)}^{\frac{1}{2}})}^{2} = 5^{2}$

Simplify the left side.

Simplify ${({(4 X^{2} - 12 X + 9)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(4 X^{2} - 12 X + 9)}^{\frac{1}{2}})}^{2}$ .

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

${(4 X^{2} - 12 X + 9)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 X^{2} - 12 X + 9)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

${(4 X^{2} - 12 X + 9)}^{1} = 5^{2}$

Simplify.

$4 X^{2} - 12 X + 9 = 5^{2}$

Simplify the right side.

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

$4 X^{2} - 12 X + 9 = 25$

Solve for $X$ .

Subtract $25$ from both sides of the equation.

$4 X^{2} - 12 X + 9 - 25 = 0$

Subtract $25$ from $9$ .

$4 X^{2} - 12 X - 16 = 0$

Factor the left side of the equation.

Factor $4$ out of $4 X^{2} - 12 X - 16$ .

Factor $4$ out of $4 X^{2}$ .

$4 (X^{2}) - 12 X - 16 = 0$

Factor $4$ out of $- 12 X$ .

$4 (X^{2}) + 4 (- 3 X) - 16 = 0$

Factor $4$ out of $- 16$ .

$4 X^{2} + 4 (- 3 X) + 4 \cdot - 4 = 0$

Factor $4$ out of $4 X^{2} + 4 (- 3 X)$ .

$4 (X^{2} - 3 X) + 4 \cdot - 4 = 0$

Factor $4$ out of $4 (X^{2} - 3 X) + 4 \cdot - 4$ .

$4 (X^{2} - 3 X - 4) = 0$

Factor.

Factor $X^{2} - 3 X - 4$ 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 $- 4$ and whose sum is $- 3$ .

$- 4, 1$

Write the factored form using these integers.

$4 ((X - 4) (X + 1)) = 0$

Remove unnecessary parentheses.

$4 (X - 4) (X + 1) = 0$

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

$X - 4 = 0$

$X + 1 = 0$

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.

$X = 4$

Set $X + 1$ equal to $0$ and solve for $X$ .

Set $X + 1$ equal to $0$ .

$X + 1 = 0$

Subtract $1$ from both sides of the equation.

$X = - 1$

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

$X = 4, - 1$

Solve for X square root of 4X^2-12X+9=5

Related Questions

Support LCMGCF.com by disabling your adblocker.