Finite Math Examples

${(2 x + 7)}^{2} - (2 x + 7) - 6 = 0$

Step 1

Simplify ${(2 x + 7)}^{2} - (2 x + 7) - 6$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite ${(2 x + 7)}^{2}$ as $(2 x + 7) (2 x + 7)$ .

$(2 x + 7) (2 x + 7) - (2 x + 7) - 6 = 0$

Step 1.1.2

Expand $(2 x + 7) (2 x + 7)$ using the FOIL Method.

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Step 1.1.2.1

Apply the distributive property.

$2 x (2 x + 7) + 7 (2 x + 7) - (2 x + 7) - 6 = 0$

Step 1.1.2.2

Apply the distributive property.

$2 x (2 x) + 2 x \cdot 7 + 7 (2 x + 7) - (2 x + 7) - 6 = 0$

Step 1.1.2.3

Apply the distributive property.

$2 x (2 x) + 2 x \cdot 7 + 7 (2 x) + 7 \cdot 7 - (2 x + 7) - 6 = 0$

Step 1.1.3

Simplify and combine like terms.

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Step 1.1.3.1

Simplify each term.

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Step 1.1.3.1.1

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 2 x \cdot 7 + 7 (2 x) + 7 \cdot 7 - (2 x + 7) - 6 = 0$

Step 1.1.3.1.2

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

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Step 1.1.3.1.2.1

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x \cdot 7 + 7 (2 x) + 7 \cdot 7 - (2 x + 7) - 6 = 0$

Step 1.1.3.1.2.2

Multiply $x$ by $x$ .

$2 \cdot 2 x^{2} + 2 x \cdot 7 + 7 (2 x) + 7 \cdot 7 - (2 x + 7) - 6 = 0$

Step 1.1.3.1.3

Multiply $2$ by $2$ .

$4 x^{2} + 2 x \cdot 7 + 7 (2 x) + 7 \cdot 7 - (2 x + 7) - 6 = 0$

Step 1.1.3.1.4

Multiply $7$ by $2$ .

$4 x^{2} + 14 x + 7 (2 x) + 7 \cdot 7 - (2 x + 7) - 6 = 0$

Step 1.1.3.1.5

Multiply $2$ by $7$ .

$4 x^{2} + 14 x + 14 x + 7 \cdot 7 - (2 x + 7) - 6 = 0$

Step 1.1.3.1.6

Multiply $7$ by $7$ .

$4 x^{2} + 14 x + 14 x + 49 - (2 x + 7) - 6 = 0$

Step 1.1.3.2

Add $14 x$ and $14 x$ .

$4 x^{2} + 28 x + 49 - (2 x + 7) - 6 = 0$

Step 1.1.4

Apply the distributive property.

$4 x^{2} + 28 x + 49 - (2 x) - 1 \cdot 7 - 6 = 0$

Step 1.1.5

Multiply $2$ by $- 1$ .

$4 x^{2} + 28 x + 49 - 2 x - 1 \cdot 7 - 6 = 0$

Step 1.1.6

Multiply $- 1$ by $7$ .

$4 x^{2} + 28 x + 49 - 2 x - 7 - 6 = 0$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $2 x$ from $28 x$ .

$4 x^{2} + 26 x + 49 - 7 - 6 = 0$

Step 1.2.2

Simplify by subtracting numbers.

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Step 1.2.2.1

Subtract $7$ from $49$ .

$4 x^{2} + 26 x + 42 - 6 = 0$

Step 1.2.2.2

Subtract $6$ from $42$ .

$4 x^{2} + 26 x + 36 = 0$

Step 2

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

$x = - \frac{9}{2}, - 2$

Step 3