Solve 8y^2-1-6y^2 4

Question

Simplify the expression

- 16 y^{2} - 1

Evaluate

8 y^{2} - 1 - 6 y^{2} \times 4

Multiply the terms

8 y^{2} - 1 - 24 y^{2}

Solution

More Steps

Evaluate

8 y^{2} - 24 y^{2}

Collect like terms by calculating the sum or difference of their coefficients

(8 - 24) y^{2}

Subtract the numbers

- 16 y^{2}

- 16 y^{2} - 1

Show Solution

y_{1} = - \frac{1}{4} i, y_{2} = \frac{1}{4} i

Alternative Form

y_{1} = - 0.25 i, y_{2} = 0.25 i

Evaluate

8 y^{2} - 1 - 6 y^{2} \times 4

To find the roots of the expression,set the expression equal to 0

8 y^{2} - 1 - 6 y^{2} \times 4 = 0

Multiply the terms

8 y^{2} - 1 - 24 y^{2} = 0

Subtract the terms

More Steps

Simplify

8 y^{2} - 1 - 24 y^{2}

Subtract the terms

More Steps

Evaluate

8 y^{2} - 24 y^{2}

Collect like terms by calculating the sum or difference of their coefficients

(8 - 24) y^{2}

Subtract the numbers

- 16 y^{2}

- 16 y^{2} - 1

- 16 y^{2} - 1 = 0

Move the constant to the right-hand side and change its sign

- 16 y^{2} = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

- 16 y^{2} = 1

Change the signs on both sides of the equation

16 y^{2} = - 1

Divide both sides

\frac{16 y ^{2}}{16} = \frac{- 1}{16}

Divide the numbers

y^{2} = \frac{- 1}{16}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

y^{2} = - \frac{1}{16}

Take the root of both sides of the equation and remember to use both positive and negative roots

y = \pm - \frac{1}{16}

Simplify the expression

More Steps

Evaluate

- \frac{1}{16}

Evaluate the power

\frac{1}{16} \times - 1

Evaluate the power

\frac{1}{16} \times i

Evaluate the power

More Steps

Evaluate

\frac{1}{16}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{1}{16}

Simplify the radical expression

\frac{1}{16}

Simplify the radical expression

\frac{1}{4}

\frac{1}{4} i

y = \pm \frac{1}{4} i

Separate the equation into 2 possible cases

y = \frac{1}{4} i y = - \frac{1}{4} i

Solution

y_{1} = - \frac{1}{4} i, y_{2} = \frac{1}{4} i

Alternative Form

y_{1} = - 0.25 i, y_{2} = 0.25 i

Show Solution