Find the Roots (Zeros) 9(2x-1)^2-8=0

$9 {(2 x - 1)}^{2} - 8 = 0$

Step 1

Simplify $9 {(2 x - 1)}^{2} - 8$ .

Simplify each term.

Rewrite ${(2 x - 1)}^{2}$ as $(2 x - 1) (2 x - 1)$ .

$9 ((2 x - 1) (2 x - 1)) - 8 = 0$

Expand $(2 x - 1) (2 x - 1)$ using the FOIL Method.

Apply the distributive property.

$9 (2 x (2 x - 1) - 1 (2 x - 1)) - 8 = 0$

Apply the distributive property.

$9 (2 x (2 x) + 2 x \cdot - 1 - 1 (2 x - 1)) - 8 = 0$

Apply the distributive property.

$9 (2 x (2 x) + 2 x \cdot - 1 - 1 (2 x) - 1 \cdot - 1) - 8 = 0$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$9 (2 \cdot 2 x \cdot x + 2 x \cdot - 1 - 1 (2 x) - 1 \cdot - 1) - 8 = 0$

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

Move $x$ .

$9 (2 \cdot 2 (x \cdot x) + 2 x \cdot - 1 - 1 (2 x) - 1 \cdot - 1) - 8 = 0$

Multiply $x$ by $x$ .

$9 (2 \cdot 2 x^{2} + 2 x \cdot - 1 - 1 (2 x) - 1 \cdot - 1) - 8 = 0$

Multiply $2$ by $2$ .

$9 (4 x^{2} + 2 x \cdot - 1 - 1 (2 x) - 1 \cdot - 1) - 8 = 0$

Multiply $- 1$ by $2$ .

$9 (4 x^{2} - 2 x - 1 (2 x) - 1 \cdot - 1) - 8 = 0$

Multiply $2$ by $- 1$ .

$9 (4 x^{2} - 2 x - 2 x - 1 \cdot - 1) - 8 = 0$

Multiply $- 1$ by $- 1$ .

$9 (4 x^{2} - 2 x - 2 x + 1) - 8 = 0$

Subtract $2 x$ from $- 2 x$ .

$9 (4 x^{2} - 4 x + 1) - 8 = 0$

Apply the distributive property.

$9 (4 x^{2}) + 9 (- 4 x) + 9 \cdot 1 - 8 = 0$

Simplify.

Multiply $4$ by $9$ .

$36 x^{2} + 9 (- 4 x) + 9 \cdot 1 - 8 = 0$

Multiply $- 4$ by $9$ .

$36 x^{2} - 36 x + 9 \cdot 1 - 8 = 0$

Multiply $9$ by $1$ .

$36 x^{2} - 36 x + 9 - 8 = 0$

Subtract $8$ from $9$ .

$36 x^{2} - 36 x + 1 = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 0.02859547, 0.97140452$

Step 3

Find the Roots (Zeros) 9(2x-1)^2-8=0

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