Algebra Examples

x^{2} - 14 x + 49

$x^{2} - 14 x + 49$

Step 1

Set

x^{2} - 14 x + 49

$x^{2} - 14 x + 49$ equal to

0

$0$ .

x^{2} - 14 x + 49 = 0

$x^{2} - 14 x + 49 = 0$

Step 2

Use the quadratic formula to find the solutions.

\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values

a = 1

$a = 1$ ,

b = - 14

$b = - 14$ , and

c = 49

$c = 49$ into the quadratic formula and solve for

x

$x$ .

\frac{14 \pm \sqrt{{(- 14)}^{2} - 4 \cdot (1 \cdot 49)}}{2 \cdot 1}

$\frac{14 \pm \sqrt{{(- 14)}^{2} - 4 \cdot (1 \cdot 49)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise

- 14

$- 14$ to the power of

2

$2$ .

x = \frac{14 \pm \sqrt{196 - 4 \cdot 1 \cdot 49}}{2 \cdot 1}

$x = \frac{14 \pm \sqrt{196 - 4 \cdot 1 \cdot 49}}{2 \cdot 1}$

Step 4.1.2

Multiply

- 4 \cdot 1 \cdot 49

$- 4 \cdot 1 \cdot 49$ .

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Step 4.1.2.1

Multiply

- 4

$- 4$ by

1

$1$ .

x = \frac{14 \pm \sqrt{196 - 4 \cdot 49}}{2 \cdot 1}

$x = \frac{14 \pm \sqrt{196 - 4 \cdot 49}}{2 \cdot 1}$

Step 4.1.2.2

Multiply

- 4

$- 4$ by

49

$49$ .

x = \frac{14 \pm \sqrt{196 - 196}}{2 \cdot 1}

$x = \frac{14 \pm \sqrt{196 - 196}}{2 \cdot 1}$

x = \frac{14 \pm \sqrt{196 - 196}}{2 \cdot 1}

$x = \frac{14 \pm \sqrt{196 - 196}}{2 \cdot 1}$

Step 4.1.3

Subtract

196

$196$ from

196

$196$ .

x = \frac{14 \pm \sqrt{0}}{2 \cdot 1}

$x = \frac{14 \pm \sqrt{0}}{2 \cdot 1}$

Step 4.1.4

Rewrite

0

$0$ as

0^{2}

$0^{2}$ .

x = \frac{14 \pm \sqrt{0^{2}}}{2 \cdot 1}

$x = \frac{14 \pm \sqrt{0^{2}}}{2 \cdot 1}$

Step 4.1.5

Pull terms out from under the radical, assuming positive real numbers.

x = \frac{14 \pm 0}{2 \cdot 1}

$x = \frac{14 \pm 0}{2 \cdot 1}$

Step 4.1.6

14

$14$ plus or minus

0

$0$ is

14

$14$ .

x = \frac{14}{2 \cdot 1}

$x = \frac{14}{2 \cdot 1}$

x = \frac{14}{2 \cdot 1}

$x = \frac{14}{2 \cdot 1}$

Step 4.2

Multiply

2

$2$ by

1

$1$ .

x = \frac{14}{2}

$x = \frac{14}{2}$

Step 4.3

Divide

14

$14$ by

2

$2$ .

x = 7

$x = 7$

x = 7

$x = 7$

Step 5

The final answer is the combination of both solutions.

x = 7

$x = 7$ Double roots