Solve Using the Quadratic Formula x^2+4x-7=0

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Algebra

$x^{2} + 4 x - 7 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 1$ , $b = 4$ , and $c = - 7$ into the quadratic formula and solve for $x$ .

$\frac{- 4 \pm \sqrt{4^{2} - 4 \cdot (1 \cdot - 7)}}{2 \cdot 1}$

Simplify.

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Simplify the numerator.

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Raise $4$ to the power of $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot 1 \cdot - 7}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot - 7}}{2 \cdot 1}$

Multiply $- 4$ by $- 7$ .

$x = \frac{- 4 \pm \sqrt{16 + 28}}{2 \cdot 1}$

Add $16$ and $28$ .

$x = \frac{- 4 \pm \sqrt{44}}{2 \cdot 1}$

Rewrite $44$ as $2^{2} \cdot 11$ .

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Factor $4$ out of $44$ .

$x = \frac{- 4 \pm \sqrt{4 (11)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 4 \pm \sqrt{2^{2} \cdot 11}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm 2 \sqrt{11}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 4 \pm 2 \sqrt{11}}{2}$

Simplify $\frac{- 4 \pm 2 \sqrt{11}}{2}$ .

$x = - 2 \pm \sqrt{11}$

The result can be shown in multiple forms.

Exact Form:

$x = - 2 \pm \sqrt{11}$

Decimal Form:

$x = 1.31662479 \dots, - 5.31662479 \dots$

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Name

Name	six hundred forty-six million three hundred forty-nine thousand twenty-three

Interesting facts

646349023 has 4 divisors, whose sum is 648110560
The reverse of 646349023 is 320943646
Previous prime number is 367

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 37
Digital Root 1

Name

Name	one billion seven hundred four million nine hundred thirty-four thousand seven hundred seventeen

Interesting facts

1704934717 has 4 divisors, whose sum is 1705112640
The reverse of 1704934717 is 7174394071
Previous prime number is 10163

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 43
Digital Root 7

Name

Name	two billion ninety-nine million one hundred ninety-eight thousand eight hundred

Interesting facts

2099198800 has 64 divisors, whose sum is 11052283788
The reverse of 2099198800 is 0088919902
Previous prime number is 25

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 46
Digital Root 1

Factor 2x^2-72

Evaluate 2 square root of 4

Solve by Completing the Square x^2+22x=31

Convert to Radical Form y^(-8/7)

Find the Roots (Zeros) f(x)=-3x^4+2x^3+7x-5