Finite Math Examples

$7 x (x + 3) - 9 = 17 x - 8$

Step 1

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

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Step 1.1

Simplify the left side.

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Apply the distributive property.

$7 x \cdot x + 7 x \cdot 3 - 9 = 17 x - 8$

Step 1.1.1.2

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

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Step 1.1.1.2.1

Move $x$ .

$7 (x \cdot x) + 7 x \cdot 3 - 9 = 17 x - 8$

Step 1.1.1.2.2

Multiply $x$ by $x$ .

$7 x^{2} + 7 x \cdot 3 - 9 = 17 x - 8$

Step 1.1.1.3

Multiply $3$ by $7$ .

$7 x^{2} + 21 x - 9 = 17 x - 8$

Step 1.2

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

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Step 1.2.1

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

$7 x^{2} + 21 x - 9 - 17 x = - 8$

Step 1.2.2

Add $8$ to both sides of the equation.

$7 x^{2} + 21 x - 9 - 17 x + 8 = 0$

Step 1.3

Simplify $7 x^{2} + 21 x - 9 - 17 x + 8$ .

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Step 1.3.1

Subtract $17 x$ from $21 x$ .

$7 x^{2} + 4 x - 9 + 8 = 0$

Step 1.3.2

Add $- 9$ and $8$ .

$7 x^{2} + 4 x - 1 = 0$

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 $a = 7$ , $b = 4$ , and $c = - 1$ into the quadratic formula and solve for $x$ .

$\frac{- 4 \pm \sqrt{4^{2} - 4 \cdot (7 \cdot - 1)}}{2 \cdot 7}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $4$ to the power of $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot 7 \cdot - 1}}{2 \cdot 7}$

Step 4.1.2

Multiply $- 4 \cdot 7 \cdot - 1$ .

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Step 4.1.2.1

Multiply $- 4$ by $7$ .

$x = \frac{- 4 \pm \sqrt{16 - 28 \cdot - 1}}{2 \cdot 7}$

Step 4.1.2.2

Multiply $- 28$ by $- 1$ .

$x = \frac{- 4 \pm \sqrt{16 + 28}}{2 \cdot 7}$

Step 4.1.3

Add $16$ and $28$ .

$x = \frac{- 4 \pm \sqrt{44}}{2 \cdot 7}$

Step 4.1.4

Rewrite $44$ as $2^{2} \cdot 11$ .

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Step 4.1.4.1

Factor $4$ out of $44$ .

$x = \frac{- 4 \pm \sqrt{4 (11)}}{2 \cdot 7}$

Step 4.1.4.2

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

$x = \frac{- 4 \pm \sqrt{2^{2} \cdot 11}}{2 \cdot 7}$

Step 4.1.5

Pull terms out from under the radical.

$x = \frac{- 4 \pm 2 \sqrt{11}}{2 \cdot 7}$

Step 4.2

Multiply $2$ by $7$ .

$x = \frac{- 4 \pm 2 \sqrt{11}}{14}$

Step 4.3

Simplify $\frac{- 4 \pm 2 \sqrt{11}}{14}$ .

$x = \frac{- 2 \pm \sqrt{11}}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 2 \pm \sqrt{11}}{7}$

Decimal Form:

$x = 0.18808925 \dots, - 0.75951782 \dots$