What are the solutions to the equation 1/4 x^2=-1/2 x+2 ?

The solutions to the equation 1/4 x^2=-1/2 x+2 are x=2,x=-4

Find the zeros of 1/4 x^2=-1/2 x+2

The zeros of 1/4 x^2=-1/2 x+2 are x=2,x=-4

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\frac{1}{4} x^{2} = - \frac{1}{2} x + 2

x = 2, x = - 4

Solution steps

\frac{1}{4} x^{2} = - \frac{1}{2} x + 2

Find Least Common Multiplier of

4, 2 : 4

Multiply by LCM=

4

\frac{1}{4} x^{2} \cdot 4 = - \frac{1}{2} x \cdot 4 + 2 \cdot 4

Simplify

x^{2} = - 2 x + 8

Move

8

to the left side

x^{2} - 8 = - 2 x

Move

2 x

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

x_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 \cdot 1 \cdot ( - 8 )}{2 \cdot 1}

2^{2} - 4 \cdot 1 \cdot (- 8) = 6

x_{1, 2} = \frac{- 2 \pm 6}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 2 + 6}{2 \cdot 1}, x_{2} = \frac{- 2 - 6}{2 \cdot 1}

x = \frac{- 2 + 6}{2 \cdot 1} : 2

x = \frac{- 2 - 6}{2 \cdot 1} : - 4

The solutions to the quadratic equation are:

x = 2, x = - 4

4 = x^{2} + 3

t^{2} + 3 = 0

x^{2} = 11 x + 126

s^{2} + 16 s + 100 = 0

x^{2} - 6 = 19

What are the solutions to the equation 1/4 x^2=-1/2 x+2 ?
The solutions to the equation 1/4 x^2=-1/2 x+2 are x=2,x=-4
Find the zeros of 1/4 x^2=-1/2 x+2
The zeros of 1/4 x^2=-1/2 x+2 are x=2,x=-4