Pre-Algebra Examples

${(3 x - 2)}^{2} = 25 x^{2}$

Step 1

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

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Step 1.1

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

$(3 x - 2) (3 x - 2) = 25 x^{2}$

Step 1.2

Expand $(3 x - 2) (3 x - 2)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$3 x (3 x - 2) - 2 (3 x - 2) = 25 x^{2}$

Step 1.2.2

Apply the distributive property.

$3 x (3 x) + 3 x \cdot - 2 - 2 (3 x - 2) = 25 x^{2}$

Step 1.2.3

Apply the distributive property.

$3 x (3 x) + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2 = 25 x^{2}$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Rewrite using the commutative property of multiplication.

$3 \cdot 3 x \cdot x + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2 = 25 x^{2}$

Step 1.3.1.2

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

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Step 1.3.1.2.1

Move $x$ .

$3 \cdot 3 (x \cdot x) + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2 = 25 x^{2}$

Step 1.3.1.2.2

Multiply $x$ by $x$ .

$3 \cdot 3 x^{2} + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2 = 25 x^{2}$

Step 1.3.1.3

Multiply $3$ by $3$ .

$9 x^{2} + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2 = 25 x^{2}$

Step 1.3.1.4

Multiply $- 2$ by $3$ .

$9 x^{2} - 6 x - 2 (3 x) - 2 \cdot - 2 = 25 x^{2}$

Step 1.3.1.5

Multiply $3$ by $- 2$ .

$9 x^{2} - 6 x - 6 x - 2 \cdot - 2 = 25 x^{2}$

Step 1.3.1.6

Multiply $- 2$ by $- 2$ .

$9 x^{2} - 6 x - 6 x + 4 = 25 x^{2}$

Step 1.3.2

Subtract $6 x$ from $- 6 x$ .

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

Step 2

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

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

Step 3