Solve Using the Quadratic Formula 4(4x-3)^2-10=26

$4 {(4 x - 3)}^{2} - 10 = 26$

Step 1

Move all terms to the left side of the equation and simplify.

Subtract $26$ from both sides of the equation.

$4 {(4 x - 3)}^{2} - 10 - 26 = 0$

Simplify $4 {(4 x - 3)}^{2} - 10 - 26$ .

Simplify each term.

Rewrite ${(4 x - 3)}^{2}$ as $(4 x - 3) (4 x - 3)$ .

$4 ((4 x - 3) (4 x - 3)) - 10 - 26 = 0$

Expand $(4 x - 3) (4 x - 3)$ using the FOIL Method.

Apply the distributive property.

$4 (4 x (4 x - 3) - 3 (4 x - 3)) - 10 - 26 = 0$

Apply the distributive property.

$4 (4 x (4 x) + 4 x \cdot - 3 - 3 (4 x - 3)) - 10 - 26 = 0$

Apply the distributive property.

$4 (4 x (4 x) + 4 x \cdot - 3 - 3 (4 x) - 3 \cdot - 3) - 10 - 26 = 0$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 (4 \cdot 4 x \cdot x + 4 x \cdot - 3 - 3 (4 x) - 3 \cdot - 3) - 10 - 26 = 0$

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

Move $x$ .

$4 (4 \cdot 4 (x \cdot x) + 4 x \cdot - 3 - 3 (4 x) - 3 \cdot - 3) - 10 - 26 = 0$

Multiply $x$ by $x$ .

$4 (4 \cdot 4 x^{2} + 4 x \cdot - 3 - 3 (4 x) - 3 \cdot - 3) - 10 - 26 = 0$

Multiply $4$ by $4$ .

$4 (16 x^{2} + 4 x \cdot - 3 - 3 (4 x) - 3 \cdot - 3) - 10 - 26 = 0$

Multiply $- 3$ by $4$ .

$4 (16 x^{2} - 12 x - 3 (4 x) - 3 \cdot - 3) - 10 - 26 = 0$

Multiply $4$ by $- 3$ .

$4 (16 x^{2} - 12 x - 12 x - 3 \cdot - 3) - 10 - 26 = 0$

Multiply $- 3$ by $- 3$ .

$4 (16 x^{2} - 12 x - 12 x + 9) - 10 - 26 = 0$

Subtract $12 x$ from $- 12 x$ .

$4 (16 x^{2} - 24 x + 9) - 10 - 26 = 0$

Apply the distributive property.

$4 (16 x^{2}) + 4 (- 24 x) + 4 \cdot 9 - 10 - 26 = 0$

Simplify.

Multiply $16$ by $4$ .

$64 x^{2} + 4 (- 24 x) + 4 \cdot 9 - 10 - 26 = 0$

Multiply $- 24$ by $4$ .

$64 x^{2} - 96 x + 4 \cdot 9 - 10 - 26 = 0$

Multiply $4$ by $9$ .

$64 x^{2} - 96 x + 36 - 10 - 26 = 0$

Subtract $10$ from $36$ .

$64 x^{2} - 96 x + 26 - 26 = 0$

Combine the opposite terms in $64 x^{2} - 96 x + 26 - 26$ .

Subtract $26$ from $26$ .

$64 x^{2} - 96 x + 0 = 0$

Add $64 x^{2} - 96 x$ and $0$ .

$64 x^{2} - 96 x = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 64$ , $b = - 96$ , and $c = 0$ into the quadratic formula and solve for $x$ .

$\frac{96 \pm \sqrt{{(- 96)}^{2} - 4 \cdot (64 \cdot 0)}}{2 \cdot 64}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 96$ to the power of $2$ .

$x = \frac{96 \pm \sqrt{9216 - 4 \cdot 64 \cdot 0}}{2 \cdot 64}$

Multiply $- 4 \cdot 64 \cdot 0$ .

Multiply $- 4$ by $64$ .

$x = \frac{96 \pm \sqrt{9216 - 256 \cdot 0}}{2 \cdot 64}$

Multiply $- 256$ by $0$ .

$x = \frac{96 \pm \sqrt{9216 + 0}}{2 \cdot 64}$

Add $9216$ and $0$ .

$x = \frac{96 \pm \sqrt{9216}}{2 \cdot 64}$

Rewrite $9216$ as $96^{2}$ .

$x = \frac{96 \pm \sqrt{96^{2}}}{2 \cdot 64}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{96 \pm 96}{2 \cdot 64}$

Multiply $2$ by $64$ .

$x = \frac{96 \pm 96}{128}$

Simplify $\frac{96 \pm 96}{128}$ .

$x = \frac{3 \pm 3}{4}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{3}{2}, 0$

Solve Using the Quadratic Formula 4(4x-3)^2-10=26

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