Solve 4((13-3y^2))

Question

Simplify the expression

52 - 12 y^{2}

Evaluate

4 (13 - 3 y^{2})

Apply the distributive property

4 \times 13 - 4 \times 3 y^{2}

Multiply the numbers

52 - 4 \times 3 y^{2}

Solution

52 - 12 y^{2}

Show Solution

y_{1} = - \frac{39}{3}, y_{2} = \frac{39}{3}

Alternative Form

y_{1} \approx - 2.081666, y_{2} \approx 2.081666

Evaluate

4 (13 - 3 y^{2})

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

4 (13 - 3 y^{2}) = 0

Rewrite the expression

13 - 3 y^{2} = 0

Rewrite the expression

- 3 y^{2} = - 13

Change the signs on both sides of the equation

3 y^{2} = 13

Divide both sides

\frac{3 y ^{2}}{3} = \frac{13}{3}

Divide the numbers

y^{2} = \frac{13}{3}

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

y = \pm \frac{13}{3}

Simplify the expression

More Steps

Evaluate

\frac{13}{3}

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

\frac{13}{3}

Multiply by the Conjugate

\frac{13 \times 3}{3 \times 3}

Multiply the numbers

More Steps

Evaluate

13 \times 3

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

13 \times 3

Calculate the product

39

\frac{39}{3 \times 3}

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

\frac{39}{3}

y = \pm \frac{39}{3}

Separate the equation into 2 possible cases

y = \frac{39}{3} y = - \frac{39}{3}

Solution

y_{1} = - \frac{39}{3}, y_{2} = \frac{39}{3}

Alternative Form

y_{1} \approx - 2.081666, y_{2} \approx 2.081666

Show Solution