Algebra Examples

$16 x^{2} - 7 x = 17 x - 9$

Step 1

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

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Step 1.1

Move all the expressions to the left side of the equation.

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Step 1.1.1

Subtract $17 x$ from both sides of the equation.

$16 x^{2} - 7 x - 17 x = - 9$

Step 1.1.2

Add $9$ to both sides of the equation.

$16 x^{2} - 7 x - 17 x + 9 = 0$

Step 1.2

Subtract $17 x$ from $- 7 x$ .

$16 x^{2} - 24 x + 9 = 0$

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 $a = 16$ , $b = - 24$ , and $c = 9$ into the quadratic formula and solve for $x$ .

$\frac{24 \pm \sqrt{{(- 24)}^{2} - 4 \cdot (16 \cdot 9)}}{2 \cdot 16}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 24$ to the power of $2$ .

$x = \frac{24 \pm \sqrt{576 - 4 \cdot 16 \cdot 9}}{2 \cdot 16}$

Step 4.1.2

Multiply $- 4 \cdot 16 \cdot 9$ .

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Step 4.1.2.1

Multiply $- 4$ by $16$ .

$x = \frac{24 \pm \sqrt{576 - 64 \cdot 9}}{2 \cdot 16}$

Step 4.1.2.2

Multiply $- 64$ by $9$ .

$x = \frac{24 \pm \sqrt{576 - 576}}{2 \cdot 16}$

Step 4.1.3

Subtract $576$ from $576$ .

$x = \frac{24 \pm \sqrt{0}}{2 \cdot 16}$

Step 4.1.4

Rewrite $0$ as $0^{2}$ .

$x = \frac{24 \pm \sqrt{0^{2}}}{2 \cdot 16}$

Step 4.1.5

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

$x = \frac{24 \pm 0}{2 \cdot 16}$

Step 4.1.6

$24$ plus or minus $0$ is $24$ .

$x = \frac{24}{2 \cdot 16}$

Step 4.2

Multiply $2$ by $16$ .

$x = \frac{24}{32}$

Step 4.3

Cancel the common factor of $24$ and $32$ .

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Step 4.3.1

Factor $8$ out of $24$ .

$x = \frac{8 (3)}{32}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $8$ out of $32$ .

$x = \frac{8 \cdot 3}{8 \cdot 4}$

Step 4.3.2.2

Cancel the common factor.

$x = \frac{8 \cdot 3}{8 \cdot 4}$

Step 4.3.2.3

Rewrite the expression.

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

Step 5

The final answer is the combination of both solutions.

$x = \frac{3}{4}$ Double roots