What are the solutions to the equation x^2+(-1/2 x)^2=6 ?

The solutions to the equation x^2+(-1/2 x)^2=6 are x=(2sqrt(6))/(sqrt(5)),x=-(2sqrt(6))/(sqrt(5))

Find the zeros of x^2+(-1/2 x)^2=6

The zeros of x^2+(-1/2 x)^2=6 are x=(2sqrt(6))/(sqrt(5)),x=-(2sqrt(6))/(sqrt(5))

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x^{2} + (- \frac{1}{2} x)^{2} = 6

x = \frac{2 6}{5}, x = - \frac{2 6}{5}

Decimal Notation

x = 2.19089 \dots, x = - 2.19089 \dots

Solution steps

x^{2} + (- \frac{1}{2} x)^{2} = 6

Expand

x^{2} + (- \frac{1}{2} x)^{2} : \frac{5}{4} x^{2}

\frac{5}{4} x^{2} = 6

Move

6

to the left side

\frac{5}{4} x^{2} - 6 = 0

Write in the standard form

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

\frac{5 x ^{2}}{4} - 6 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 0 \pm 0 ^{2} - 4 \cdot \frac{5}{4} ( - 6 )}{2 \cdot \frac{5}{4}}

0^{2} - 4 \cdot \frac{5}{4} (- 6) = 30

x_{1, 2} = \frac{- 0 \pm 30}{2 \cdot \frac{5}{4}}

Separate the solutions

x_{1} = \frac{- 0 + 30}{2 \cdot \frac{5}{4}}, x_{2} = \frac{- 0 - 30}{2 \cdot \frac{5}{4}}

x = \frac{- 0 + 30}{2 \frac{5}{4}} : \frac{2 6}{5}

x = \frac{- 0 - 30}{2 \frac{5}{4}} : - \frac{2 6}{5}

The solutions to the quadratic equation are:

x = \frac{2 6}{5}, x = - \frac{2 6}{5}

5 x^{2} + 1 = 6

y, (x - 1)^{2} + y^{2} = 25

7 x^{2} + (2 k - 1) x - 3 k + 2 = 0

5 x^{2} - 11 = 49

3 w^{2} - 3 w - 6 = - 2

What are the solutions to the equation x^2+(-1/2 x)^2=6 ?
The solutions to the equation x^2+(-1/2 x)^2=6 are x=(2sqrt(6))/(sqrt(5)),x=-(2sqrt(6))/(sqrt(5))
Find the zeros of x^2+(-1/2 x)^2=6
The zeros of x^2+(-1/2 x)^2=6 are x=(2sqrt(6))/(sqrt(5)),x=-(2sqrt(6))/(sqrt(5))