Pre-Algebra Examples

$16 x^{2} - 15 x + 14 = 15 x^{2} - 11 x + 10$

Step 1

Move all terms containing $x$ to the left side of the equation.

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Step 1.1

Subtract $15 x^{2}$ from both sides of the equation.

$16 x^{2} - 15 x + 14 - 15 x^{2} = - 11 x + 10$

Step 1.2

Add $11 x$ to both sides of the equation.

$16 x^{2} - 15 x + 14 - 15 x^{2} + 11 x = 10$

Step 1.3

Subtract $15 x^{2}$ from $16 x^{2}$ .

$x^{2} - 15 x + 14 + 11 x = 10$

Step 1.4

Add $- 15 x$ and $11 x$ .

$x^{2} - 4 x + 14 = 10$

Step 2

Subtract $10$ from both sides of the equation.

$x^{2} - 4 x + 14 - 10 = 0$

Step 3

Subtract $10$ from $14$ .

$x^{2} - 4 x + 4 = 0$

Step 4

Factor using the perfect square rule.

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Step 4.1

Rewrite $4$ as $2^{2}$ .

$x^{2} - 4 x + 2^{2} = 0$

Step 4.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 x = 2 \cdot x \cdot 2$

Step 4.3

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot 2 + 2^{2} = 0$

Step 4.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 2$ .

${(x - 2)}^{2} = 0$

Step 5

Set the $x - 2$ equal to $0$ .

$x - 2 = 0$

Step 6

Add $2$ to both sides of the equation.

$x = 2$