Algebra Examples

$9 - 7 x = {(4 x - 3)}^{2} + 5$

Step 1

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

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Step 1.1

Simplify the right side.

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Step 1.1.1

Simplify ${(4 x - 3)}^{2} + 5$ .

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Step 1.1.1.1

Simplify each term.

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Step 1.1.1.1.1

Rewrite ${(4 x - 3)}^{2}$ as $(4 x - 3) (4 x - 3)$ .

$9 - 7 x = (4 x - 3) (4 x - 3) + 5$

Step 1.1.1.1.2

Expand $(4 x - 3) (4 x - 3)$ using the FOIL Method.

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Step 1.1.1.1.2.1

Apply the distributive property.

$9 - 7 x = 4 x (4 x - 3) - 3 (4 x - 3) + 5$

Step 1.1.1.1.2.2

Apply the distributive property.

$9 - 7 x = 4 x (4 x) + 4 x \cdot - 3 - 3 (4 x - 3) + 5$

Step 1.1.1.1.2.3

Apply the distributive property.

$9 - 7 x = 4 x (4 x) + 4 x \cdot - 3 - 3 (4 x) - 3 \cdot - 3 + 5$

Step 1.1.1.1.3

Simplify and combine like terms.

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Step 1.1.1.1.3.1

Simplify each term.

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Step 1.1.1.1.3.1.1

Rewrite using the commutative property of multiplication.

$9 - 7 x = 4 \cdot 4 x \cdot x + 4 x \cdot - 3 - 3 (4 x) - 3 \cdot - 3 + 5$

Step 1.1.1.1.3.1.2

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

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Step 1.1.1.1.3.1.2.1

Move $x$ .

$9 - 7 x = 4 \cdot 4 (x \cdot x) + 4 x \cdot - 3 - 3 (4 x) - 3 \cdot - 3 + 5$

Step 1.1.1.1.3.1.2.2

Multiply $x$ by $x$ .

$9 - 7 x = 4 \cdot 4 x^{2} + 4 x \cdot - 3 - 3 (4 x) - 3 \cdot - 3 + 5$

Step 1.1.1.1.3.1.3

Multiply $4$ by $4$ .

$9 - 7 x = 16 x^{2} + 4 x \cdot - 3 - 3 (4 x) - 3 \cdot - 3 + 5$

Step 1.1.1.1.3.1.4

Multiply $- 3$ by $4$ .

$9 - 7 x = 16 x^{2} - 12 x - 3 (4 x) - 3 \cdot - 3 + 5$

Step 1.1.1.1.3.1.5

Multiply $4$ by $- 3$ .

$9 - 7 x = 16 x^{2} - 12 x - 12 x - 3 \cdot - 3 + 5$

Step 1.1.1.1.3.1.6

Multiply $- 3$ by $- 3$ .

$9 - 7 x = 16 x^{2} - 12 x - 12 x + 9 + 5$

Step 1.1.1.1.3.2

Subtract $12 x$ from $- 12 x$ .

$9 - 7 x = 16 x^{2} - 24 x + 9 + 5$

Step 1.1.1.2

Add $9$ and $5$ .

$9 - 7 x = 16 x^{2} - 24 x + 14$

Step 1.2

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

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Step 1.2.1

Subtract $16 x^{2}$ from both sides of the equation.

$9 - 7 x - 16 x^{2} = - 24 x + 14$

Step 1.2.2

Add $24 x$ to both sides of the equation.

$9 - 7 x - 16 x^{2} + 24 x = 14$

Step 1.2.3

Subtract $14$ from both sides of the equation.

$9 - 7 x - 16 x^{2} + 24 x - 14 = 0$

Step 1.3

Simplify $9 - 7 x - 16 x^{2} + 24 x - 14$ .

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Step 1.3.1

Subtract $14$ from $9$ .

$- 7 x - 16 x^{2} + 24 x - 5 = 0$

Step 1.3.2

Add $- 7 x$ and $24 x$ .

$- 16 x^{2} + 17 x - 5 = 0$

Step 2

Once the quadratic is in standard form, the values of $a$ , $b$ , and $c$ can be found.

$a x^{2} + b x + c$

Step 3

Use the standard form of the equation to find $a$ , $b$ , and $c$ for this quadratic.

$a = - 16$ , $b = 17$ , $c = - 5$