Solve 2x^2+8x-y+8=0 | Microsoft Math Solver

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Solve for x

x = \frac{2 y}{2} - 2

x = - \frac{2 y}{2} - 2, y \geq 0

Steps Using the Quadratic Formula

Steps for Completing the Square

Steps Using the Quadratic Formula

2 x^{2} + 8 x - y + 8 = 0

All equations of the form

a x^{2} + b x + c = 0

can be solved using the quadratic formula:

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

. The quadratic formula gives two solutions, one when

\pm

is addition and one when it is subtraction.

2 x^{2} + 8 x + 8 - y = 0

This equation is in standard form:

a x^{2} + b x + c = 0

. Substitute

2

for

a

,

8

for

b

, and

- y + 8

for

c

in the quadratic formula,

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

.

x = \frac{- 8 \pm 8 ^{2} - 4 \times 2 ( 8 - y )}{2 \times 2}

Square

8

.

x = \frac{- 8 \pm 6 4 - 4 \times 2 ( 8 - y )}{2 \times 2}

Multiply

- 4

times

2

.

x = \frac{- 8 \pm 6 4 - 8 ( 8 - y )}{2 \times 2}

Multiply

- 8

times

- y + 8

.

x = \frac{- 8 \pm 6 4 + 8 y - 6 4}{2 \times 2}

Add

64

to

8 y - 64

.

x = \frac{- 8 \pm 8 y}{2 \times 2}

Take the square root of

8 y

.

x = \frac{- 8 \pm 2 2 y}{2 \times 2}

Multiply

2

times

2

.

x = \frac{- 8 \pm 2 2 y}{4}

Now solve the equation

x = \frac{- 8 \pm 2 2 y}{4}

when

\pm

is plus. Add

- 8

to

2 2 y

.

x = \frac{2 2 y - 8}{4}

Divide

- 8 + 2 2 y

by

4

.

x = \frac{2 y}{2} - 2

Now solve the equation

x = \frac{- 8 \pm 2 2 y}{4}

when

\pm

is minus. Subtract

2 2 y

from

- 8

.

x = \frac{- 2 2 y - 8}{4}

Divide

- 8 - 2 2 y

by

4

.

x = - \frac{2 y}{2} - 2

The equation is now solved.

x = \frac{2 y}{2} - 2

x = - \frac{2 y}{2} - 2

Solve for y

y = 2 (x + 2)^{2}

Steps for Solving Linear Equation

2 x^{2} + 8 x - y + 8 = 0

Subtract

2 x^{2}

from both sides. Anything subtracted from zero gives its negation.

8 x - y + 8 = - 2 x^{2}

Subtract

8 x

from both sides.

- y + 8 = - 2 x^{2} - 8 x

Subtract

8

from both sides.

- y = - 2 x^{2} - 8 x - 8

Divide both sides by

- 1

.

\frac{- y}{- 1} = - \frac{2 ( x + 2 ) ^{2}}{- 1}

Dividing by

- 1

undoes the multiplication by

- 1

.

y = - \frac{2 ( x + 2 ) ^{2}}{- 1}

Divide

- 2 (2 + x)^{2}

by

- 1

.

y = 2 (x + 2)^{2}

Solve for x (complex solution)

x = \frac{2 y}{2} - 2

x = - \frac{2 y}{2} - 2

Graph

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2 x^{2} + 8 x - y + 8 = 0

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2x^{2}+8x+8-y=0

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

x=\frac{-8±\sqrt{8^{2}-4\times 2\left(8-y\right)}}{2\times 2}

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 8 for b, and -y+8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

x=\frac{-8±\sqrt{64-4\times 2\left(8-y\right)}}{2\times 2}

Square 8.

x=\frac{-8±\sqrt{64-8\left(8-y\right)}}{2\times 2}

Multiply -4 times 2.

x=\frac{-8±\sqrt{64+8y-64}}{2\times 2}

Multiply -8 times -y+8.

x=\frac{-8±\sqrt{8y}}{2\times 2}

Add 64 to 8y-64.

x=\frac{-8±2\sqrt{2y}}{2\times 2}

Take the square root of 8y.

x=\frac{-8±2\sqrt{2y}}{4}

Multiply 2 times 2.

x=\frac{2\sqrt{2y}-8}{4}

Now solve the equation x=\frac{-8±2\sqrt{2y}}{4} when ± is plus. Add -8 to 2\sqrt{2y}.

x=\frac{\sqrt{2y}}{2}-2

Divide -8+2\sqrt{2y} by 4.

x=\frac{-2\sqrt{2y}-8}{4}

Now solve the equation x=\frac{-8±2\sqrt{2y}}{4} when ± is minus. Subtract 2\sqrt{2y} from -8.

x=-\frac{\sqrt{2y}}{2}-2

Divide -8-2\sqrt{2y} by 4.

x=\frac{\sqrt{2y}}{2}-2 x=-\frac{\sqrt{2y}}{2}-2

The equation is now solved.

2x^{2}+8x+8-y=0

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

2x^{2}+8x+8-y-\left(8-y\right)=-\left(8-y\right)

Subtract -y+8 from both sides of the equation.

2x^{2}+8x=-\left(8-y\right)

Subtracting -y+8 from itself leaves 0.

2x^{2}+8x=y-8

Subtract -y+8 from 0.

\frac{2x^{2}+8x}{2}=\frac{y-8}{2}

Divide both sides by 2.

x^{2}+\frac{8}{2}x=\frac{y-8}{2}

Dividing by 2 undoes the multiplication by 2.

x^{2}+4x=\frac{y-8}{2}

Divide 8 by 2.

x^{2}+4x=\frac{y}{2}-4

Divide y-8 by 2.

x^{2}+4x+2^{2}=\frac{y}{2}-4+2^{2}

Divide 4, the coefficient of the x term, by 2 to get 2. Then add the square of 2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

x^{2}+4x+4=\frac{y}{2}-4+4

Square 2.

x^{2}+4x+4=\frac{y}{2}

Add \frac{y}{2}-4 to 4.

\left(x+2\right)^{2}=\frac{y}{2}

Factor x^{2}+4x+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

\sqrt{\left(x+2\right)^{2}}=\sqrt{\frac{y}{2}}

Take the square root of both sides of the equation.

x+2=\frac{\sqrt{2y}}{2} x+2=-\frac{\sqrt{2y}}{2}

Simplify.

x=\frac{\sqrt{2y}}{2}-2 x=-\frac{\sqrt{2y}}{2}-2

Subtract 2 from both sides of the equation.

8x-y+8=-2x^{2}

Subtract 2x^{2} from both sides. Anything subtracted from zero gives its negation.

-y+8=-2x^{2}-8x

Subtract 8x from both sides.

-y=-2x^{2}-8x-8

Subtract 8 from both sides.

\frac{-y}{-1}=-\frac{2\left(x+2\right)^{2}}{-1}

Divide both sides by -1.

y=-\frac{2\left(x+2\right)^{2}}{-1}

Dividing by -1 undoes the multiplication by -1.

y=2\left(x+2\right)^{2}

Divide -2\left(2+x\right)^{2} by -1.

Examples

Quadratic equation

x^{2} - 4 x - 5 = 0

4 sin θ cos θ = 2 sin θ

Linear equation

y = 3 x + 4

699 * 533

[2534] [2 - 1 0135]

Simultaneous equation

{8 x + 2 y = 46 7 x + 3 y = 47

Differentiation

\frac{d}{d x} \frac{( 3 x ^{2} - 2 )}{( x - 5 )}

\int_{0}^{1} x e^{- x^{2}} d x

x \to - 3 lim \frac{x ^{2} - 9}{x ^{2} + 2 x - 3}

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