Algebra Examples

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

Step 1

Simplify the equation into a proper form to complete the square.

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Step 1.1

Add $5$ to both sides of the equation.

$2 x^{2} + 2 x = x^{2} + 5$

Step 1.2

Move all terms containing $x$ to the left side of the equation.

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Step 1.2.1

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

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

Step 1.2.2

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

$x^{2} + 2 x = 5$

Step 2

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

${(\frac{b}{2})}^{2} = {(1)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} + 2 x + {(1)}^{2} = 5 + {(1)}^{2}$

Step 4

Simplify the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

One to any power is one.

$x^{2} + 2 x + 1 = 5 + {(1)}^{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $5 + {(1)}^{2}$ .

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Step 4.2.1.1

One to any power is one.

$x^{2} + 2 x + 1 = 5 + 1$

Step 4.2.1.2

Add $5$ and $1$ .

$x^{2} + 2 x + 1 = 6$

Step 5

Factor the perfect trinomial square into ${(x + 1)}^{2}$ .

${(x + 1)}^{2} = 6$

Step 6

Solve the equation for $x$ .

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Step 6.1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x + 1 = \pm \sqrt{6}$

Step 6.2

Subtract $1$ from both sides of the equation.

$x = \pm \sqrt{6} - 1$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{6} - 1$

Decimal Form:

$x = 1.44948974 \dots, - 3.44948974 \dots$