Algebra Examples

$x^{2} - 7 x + c = {(x + a)}^{2}$

Step 1

Simplify ${(x + a)}^{2}$ .

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Step 1.1

Rewrite.

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

Step 1.2

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

$x^{2} - 7 x + c = (x + a) (x + a)$

Step 1.3

Expand $(x + a) (x + a)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$x^{2} - 7 x + c = x (x + a) + a (x + a)$

Step 1.3.2

Apply the distributive property.

$x^{2} - 7 x + c = x \cdot x + x a + a (x + a)$

Step 1.3.3

Apply the distributive property.

$x^{2} - 7 x + c = x \cdot x + x a + a x + a \cdot a$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $x$ by $x$ .

$x^{2} - 7 x + c = x^{2} + x a + a x + a \cdot a$

Step 1.4.1.2

Multiply $a$ by $a$ .

$x^{2} - 7 x + c = x^{2} + x a + a x + a^{2}$

Step 1.4.2

Add $x a$ and $a x$ .

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Step 1.4.2.1

Reorder $x$ and $a$ .

$x^{2} - 7 x + c = x^{2} + a x + a x + a^{2}$

Step 1.4.2.2

Add $a x$ and $a x$ .

$x^{2} - 7 x + c = x^{2} + 2 a x + a^{2}$

Step 2

Move all terms not containing $c$ to the right side of the equation.

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Step 2.1

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

$- 7 x + c = x^{2} + 2 a x + a^{2} - x^{2}$

Step 2.2

Add $7 x$ to both sides of the equation.

$c = x^{2} + 2 a x + a^{2} - x^{2} + 7 x$

Step 2.3

Combine the opposite terms in $x^{2} + 2 a x + a^{2} - x^{2} + 7 x$ .

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Step 2.3.1

Subtract $x^{2}$ from $x^{2}$ .

$c = 2 a x + a^{2} + 0 + 7 x$

Step 2.3.2

Add $2 a x + a^{2}$ and $0$ .

$c = 2 a x + a^{2} + 7 x$