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

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

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

Subtract $26$ from both sides of the equation.

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

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

Simplify each term.

Rewrite ${(4 x - 10)}^{2}$ as $(4 x - 10) (4 x - 10)$ .

$2 ((4 x - 10) (4 x - 10)) - 26 = 0$

Expand $(4 x - 10) (4 x - 10)$ using the FOIL Method.

Apply the distributive property.

$2 (4 x (4 x - 10) - 10 (4 x - 10)) - 26 = 0$

Apply the distributive property.

$2 (4 x (4 x) + 4 x \cdot - 10 - 10 (4 x - 10)) - 26 = 0$

Apply the distributive property.

$2 (4 x (4 x) + 4 x \cdot - 10 - 10 (4 x) - 10 \cdot - 10) - 26 = 0$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 (4 \cdot 4 x \cdot x + 4 x \cdot - 10 - 10 (4 x) - 10 \cdot - 10) - 26 = 0$

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

Move $x$ .

$2 (4 \cdot 4 (x \cdot x) + 4 x \cdot - 10 - 10 (4 x) - 10 \cdot - 10) - 26 = 0$

Multiply $x$ by $x$ .

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

Multiply $4$ by $4$ .

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

Multiply $- 10$ by $4$ .

$2 (16 x^{2} - 40 x - 10 (4 x) - 10 \cdot - 10) - 26 = 0$

Multiply $4$ by $- 10$ .

$2 (16 x^{2} - 40 x - 40 x - 10 \cdot - 10) - 26 = 0$

Multiply $- 10$ by $- 10$ .

$2 (16 x^{2} - 40 x - 40 x + 100) - 26 = 0$

Subtract $40 x$ from $- 40 x$ .

$2 (16 x^{2} - 80 x + 100) - 26 = 0$

Apply the distributive property.

$2 (16 x^{2}) + 2 (- 80 x) + 2 \cdot 100 - 26 = 0$

Simplify.

Multiply $16$ by $2$ .

$32 x^{2} + 2 (- 80 x) + 2 \cdot 100 - 26 = 0$

Multiply $- 80$ by $2$ .

$32 x^{2} - 160 x + 2 \cdot 100 - 26 = 0$

Multiply $2$ by $100$ .

$32 x^{2} - 160 x + 200 - 26 = 0$

Subtract $26$ from $200$ .

$32 x^{2} - 160 x + 174 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 32$ , $b = - 160$ , and $c = 174$ into the quadratic formula and solve for $x$ .

$\frac{160 \pm \sqrt{{(- 160)}^{2} - 4 \cdot (32 \cdot 174)}}{2 \cdot 32}$

Simplify.

Simplify the numerator.

Raise $- 160$ to the power of $2$ .

$x = \frac{160 \pm \sqrt{25600 - 4 \cdot 32 \cdot 174}}{2 \cdot 32}$

Multiply $- 4$ by $32$ .

$x = \frac{160 \pm \sqrt{25600 - 128 \cdot 174}}{2 \cdot 32}$

Multiply $- 128$ by $174$ .

$x = \frac{160 \pm \sqrt{25600 - 22272}}{2 \cdot 32}$

Subtract $22272$ from $25600$ .

$x = \frac{160 \pm \sqrt{3328}}{2 \cdot 32}$

Rewrite $3328$ as $16^{2} \cdot 13$ .

Factor $256$ out of $3328$ .

$x = \frac{160 \pm \sqrt{256 (13)}}{2 \cdot 32}$

Rewrite $256$ as $16^{2}$ .

$x = \frac{160 \pm \sqrt{16^{2} \cdot 13}}{2 \cdot 32}$

Pull terms out from under the radical.

$x = \frac{160 \pm 16 \sqrt{13}}{2 \cdot 32}$

Multiply $2$ by $32$ .

$x = \frac{160 \pm 16 \sqrt{13}}{64}$

Simplify $\frac{160 \pm 16 \sqrt{13}}{64}$ .

$x = \frac{10 \pm \sqrt{13}}{4}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{10 \pm \sqrt{13}}{4}$

Decimal Form:

$x = 3.40138781 \dots, 1.59861218 \dots$

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

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