Algebra Examples

$4 x^{2} + 28 x + 49 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 4$ , $b = 28$ , and $c = 49$ into the quadratic formula and solve for $x$ .

$\frac{- 28 \pm \sqrt{28^{2} - 4 \cdot (4 \cdot 49)}}{2 \cdot 4}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Raise $28$ to the power of $2$ .

$x = \frac{- 28 \pm \sqrt{784 - 4 \cdot 4 \cdot 49}}{2 \cdot 4}$

Step 3.1.2

Multiply $- 4 \cdot 4 \cdot 49$ .

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Step 3.1.2.1

Multiply $- 4$ by $4$ .

$x = \frac{- 28 \pm \sqrt{784 - 16 \cdot 49}}{2 \cdot 4}$

Step 3.1.2.2

Multiply $- 16$ by $49$ .

$x = \frac{- 28 \pm \sqrt{784 - 784}}{2 \cdot 4}$

Step 3.1.3

Subtract $784$ from $784$ .

$x = \frac{- 28 \pm \sqrt{0}}{2 \cdot 4}$

Step 3.1.4

Rewrite $0$ as $0^{2}$ .

$x = \frac{- 28 \pm \sqrt{0^{2}}}{2 \cdot 4}$

Step 3.1.5

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

$x = \frac{- 28 \pm 0}{2 \cdot 4}$

Step 3.1.6

$- 28$ plus or minus $0$ is $- 28$ .

$x = \frac{- 28}{2 \cdot 4}$

Step 3.2

Multiply $2$ by $4$ .

$x = \frac{- 28}{8}$

Step 3.3

Cancel the common factor of $- 28$ and $8$ .

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Step 3.3.1

Factor $4$ out of $- 28$ .

$x = \frac{4 (- 7)}{8}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $4$ out of $8$ .

$x = \frac{4 \cdot - 7}{4 \cdot 2}$

Step 3.3.2.2

Cancel the common factor.

$x = \frac{4 \cdot - 7}{4 \cdot 2}$

Step 3.3.2.3

Rewrite the expression.

$x = \frac{- 7}{2}$

Step 3.4

Move the negative in front of the fraction.

$x = - \frac{7}{2}$

Step 4

The final answer is the combination of both solutions.

$x = - \frac{7}{2}$ Double roots