Precalculus Examples

$x^{2} - 2 x - 6 = 0$

Step 1

Add $6$ to both sides of the equation.

$x^{2} - 2 x = 6$

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.

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

Step 4

Simplify the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Raise $- 1$ to the power of $2$ .

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

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $6 + {(- 1)}^{2}$ .

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Step 4.2.1.1

Raise $- 1$ to the power of $2$ .

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

Step 4.2.1.2

Add $6$ and $1$ .

$x^{2} - 2 x + 1 = 7$

Step 5

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

${(x - 1)}^{2} = 7$

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.

$x - 1 = \pm \sqrt{7}$

Step 6.2

Add $1$ to both sides of the equation.

$x = \pm \sqrt{7} + 1$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{7} + 1$

Decimal Form:

$x = 3.64575131 \dots, - 1.64575131 \dots$