Algebra Examples

$(5 + x) (5 - x) = 7$

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 $(5 + x) (5 - x)$ .

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Step 1.1.1.1

Expand $(5 + x) (5 - x)$ using the FOIL Method.

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Step 1.1.1.1.1

Apply the distributive property.

$5 (5 - x) + x (5 - x) = 7$

Step 1.1.1.1.2

Apply the distributive property.

$5 \cdot 5 + 5 (- x) + x (5 - x) = 7$

Step 1.1.1.1.3

Apply the distributive property.

$5 \cdot 5 + 5 (- x) + x \cdot 5 + x (- x) = 7$

Step 1.1.1.2

Simplify and combine like terms.

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Step 1.1.1.2.1

Simplify each term.

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Step 1.1.1.2.1.1

Multiply $5$ by $5$ .

$25 + 5 (- x) + x \cdot 5 + x (- x) = 7$

Step 1.1.1.2.1.2

Multiply $- 1$ by $5$ .

$25 - 5 x + x \cdot 5 + x (- x) = 7$

Step 1.1.1.2.1.3

Move $5$ to the left of $x$ .

$25 - 5 x + 5 \cdot x + x (- x) = 7$

Step 1.1.1.2.1.4

Rewrite using the commutative property of multiplication.

$25 - 5 x + 5 x - x \cdot x = 7$

Step 1.1.1.2.1.5

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

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Step 1.1.1.2.1.5.1

Move $x$ .

$25 - 5 x + 5 x - (x \cdot x) = 7$

Step 1.1.1.2.1.5.2

Multiply $x$ by $x$ .

$25 - 5 x + 5 x - x^{2} = 7$

Step 1.1.1.2.2

Add $- 5 x$ and $5 x$ .

$25 + 0 - x^{2} = 7$

Step 1.1.1.2.3

Add $25$ and $0$ .

$25 - x^{2} = 7$

Step 1.2

Subtract $7$ from both sides of the equation.

$25 - x^{2} - 7 = 0$

Step 1.3

Subtract $7$ from $25$ .

$- x^{2} + 18 = 0$

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.

$a = - 1$ , $b = 0$ , $c = 18$