Algebra Examples

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

Step 1

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

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Step 1.1

Subtract ${(4 x - 3)}^{2}$ from both sides of the equation.

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

Step 1.2

Subtract $5$ from both sides of the equation.

$9 - 7 x - {(4 x - 3)}^{2} - 5 = 0$

Step 2

Simplify $9 - 7 x - {(4 x - 3)}^{2} - 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$9 - 7 x - ((4 x - 3) (4 x - 3)) - 5 = 0$

Step 2.1.2

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

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Step 2.1.2.1

Apply the distributive property.

$9 - 7 x - (4 x (4 x - 3) - 3 (4 x - 3)) - 5 = 0$

Step 2.1.2.2

Apply the distributive property.

$9 - 7 x - (4 x (4 x) + 4 x \cdot - 3 - 3 (4 x - 3)) - 5 = 0$

Step 2.1.2.3

Apply the distributive property.

$9 - 7 x - (4 x (4 x) + 4 x \cdot - 3 - 3 (4 x) - 3 \cdot - 3) - 5 = 0$

Step 2.1.3

Simplify and combine like terms.

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Step 2.1.3.1

Simplify each term.

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Step 2.1.3.1.1

Rewrite using the commutative property of multiplication.

$9 - 7 x - (4 \cdot 4 x \cdot x + 4 x \cdot - 3 - 3 (4 x) - 3 \cdot - 3) - 5 = 0$

Step 2.1.3.1.2

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

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Step 2.1.3.1.2.1

Move $x$ .

$9 - 7 x - (4 \cdot 4 (x \cdot x) + 4 x \cdot - 3 - 3 (4 x) - 3 \cdot - 3) - 5 = 0$

Step 2.1.3.1.2.2

Multiply $x$ by $x$ .

$9 - 7 x - (4 \cdot 4 x^{2} + 4 x \cdot - 3 - 3 (4 x) - 3 \cdot - 3) - 5 = 0$

Step 2.1.3.1.3

Multiply $4$ by $4$ .

$9 - 7 x - (16 x^{2} + 4 x \cdot - 3 - 3 (4 x) - 3 \cdot - 3) - 5 = 0$

Step 2.1.3.1.4

Multiply $- 3$ by $4$ .

$9 - 7 x - (16 x^{2} - 12 x - 3 (4 x) - 3 \cdot - 3) - 5 = 0$

Step 2.1.3.1.5

Multiply $4$ by $- 3$ .

$9 - 7 x - (16 x^{2} - 12 x - 12 x - 3 \cdot - 3) - 5 = 0$

Step 2.1.3.1.6

Multiply $- 3$ by $- 3$ .

$9 - 7 x - (16 x^{2} - 12 x - 12 x + 9) - 5 = 0$

Step 2.1.3.2

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

$9 - 7 x - (16 x^{2} - 24 x + 9) - 5 = 0$

Step 2.1.4

Apply the distributive property.

$9 - 7 x - (16 x^{2}) - (- 24 x) - 1 \cdot 9 - 5 = 0$

Step 2.1.5

Simplify.

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Step 2.1.5.1

Multiply $16$ by $- 1$ .

$9 - 7 x - 16 x^{2} - (- 24 x) - 1 \cdot 9 - 5 = 0$

Step 2.1.5.2

Multiply $- 24$ by $- 1$ .

$9 - 7 x - 16 x^{2} + 24 x - 1 \cdot 9 - 5 = 0$

Step 2.1.5.3

Multiply $- 1$ by $9$ .

$9 - 7 x - 16 x^{2} + 24 x - 9 - 5 = 0$

Step 2.2

Combine the opposite terms in $9 - 7 x - 16 x^{2} + 24 x - 9 - 5$ .

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Step 2.2.1

Subtract $9$ from $9$ .

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

Step 2.2.2

Add $- 7 x - 16 x^{2} + 24 x$ and $0$ .

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

Step 2.3

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

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

Step 3

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c = 0$

Step 4

The standard form is $- 16 x^{2} + 17 x - 5$ .

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

Step 5