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

Question

Simplify the expression

8 y^{2} - 145

Evaluate

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

Multiply the terms

More Steps

Evaluate

- 6^{2} \times 4

Evaluate the power

- 36 \times 4

Multiply the numbers

- 144

8 y^{2} - 1 - 144

Solution

8 y^{2} - 145

Show Solution

y_{1} = - \frac{290}{4}, y_{2} = \frac{290}{4}

Alternative Form

y_{1} \approx - 4.257347, y_{2} \approx 4.257347

Evaluate

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

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

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

Multiply the terms

More Steps

Evaluate

6^{2} \times 4

Evaluate the power

36 \times 4

Multiply the numbers

144

8 y^{2} - 1 - 144 = 0

Subtract the numbers

8 y^{2} - 145 = 0

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

8 y^{2} = 0 + 145

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

8 y^{2} = 145

Divide both sides

\frac{8 y ^{2}}{8} = \frac{145}{8}

Divide the numbers

y^{2} = \frac{145}{8}

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

y = \pm \frac{145}{8}

Simplify the expression

More Steps

Evaluate

\frac{145}{8}

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

\frac{145}{8}

Simplify the radical expression

More Steps

Evaluate

8

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 2

Write the number in exponential form with the base of 2

2^{2} \times 2

The root of a product is equal to the product of the roots of each factor

2^{2} \times 2

Reduce the index of the radical and exponent with 2

22

\frac{145}{2 2}

Multiply by the Conjugate

\frac{145 \times 2}{2 2 \times 2}

Multiply the numbers

More Steps

Evaluate

145 \times 2

The product of roots with the same index is equal to the root of the product

145 \times 2

Calculate the product

290

\frac{290}{2 2 \times 2}

Multiply the numbers

More Steps

Evaluate

22 \times 2

When a square root of an expression is multiplied by itself,the result is that expression

2 \times 2

Multiply the numbers

4

\frac{290}{4}

y = \pm \frac{290}{4}

Separate the equation into 2 possible cases

y = \frac{290}{4} y = - \frac{290}{4}

Solution

y_{1} = - \frac{290}{4}, y_{2} = \frac{290}{4}

Alternative Form

y_{1} \approx - 4.257347, y_{2} \approx 4.257347

Show Solution