Solve 4 - 2[6 - (7y^2)] - 3

Question

Simplify the expression

- 11 + 14 y^{2}

Evaluate

4 - 2 (6 - 7 y^{2}) - 3

Expand the expression

More Steps

Calculate

- 2 (6 - 7 y^{2})

Apply the distributive property

- 2 \times 6 - (- 2 \times 7 y^{2})

Multiply the numbers

- 12 - (- 2 \times 7 y^{2})

Multiply the numbers

- 12 - (- 14 y^{2})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 12 + 14 y^{2}

4 - 12 + 14 y^{2} - 3

Solution

- 11 + 14 y^{2}

Show Solution

Find the roots

y_{1} = - \frac{154}{14}, y_{2} = \frac{154}{14}

Alternative Form

y_{1} \approx - 0.886405, y_{2} \approx 0.886405

Evaluate

4 - 2 (6 - (7 y^{2})) - 3

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

4 - 2 (6 - (7 y^{2})) - 3 = 0

Multiply the terms

4 - 2 (6 - 7 y^{2}) - 3 = 0

Subtract the terms

More Steps

Simplify

4 - 2 (6 - 7 y^{2})

Expand the expression

More Steps

Calculate

- 2 (6 - 7 y^{2})

Apply the distributive property

- 2 \times 6 - (- 2 \times 7 y^{2})

Multiply the numbers

- 12 - (- 2 \times 7 y^{2})

Multiply the numbers

- 12 - (- 14 y^{2})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 12 + 14 y^{2}

4 - 12 + 14 y^{2}

Subtract the numbers

- 8 + 14 y^{2}

- 8 + 14 y^{2} - 3 = 0

Subtract the numbers

- 11 + 14 y^{2} = 0

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

14 y^{2} = 0 + 11

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

14 y^{2} = 11

Divide both sides

\frac{14 y ^{2}}{14} = \frac{11}{14}

Divide the numbers

y^{2} = \frac{11}{14}

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

y = \pm \frac{11}{14}

Simplify the expression

More Steps

Evaluate

\frac{11}{14}

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

\frac{11}{14}

Multiply by the Conjugate

\frac{11 \times 14}{14 \times 14}

Multiply the numbers

More Steps

Evaluate

11 \times 14

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

11 \times 14

Calculate the product

154

\frac{154}{14 \times 14}

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

\frac{154}{14}

y = \pm \frac{154}{14}

Separate the equation into 2 possible cases

y = \frac{154}{14} y = - \frac{154}{14}

Solution

y_{1} = - \frac{154}{14}, y_{2} = \frac{154}{14}

Alternative Form

y_{1} \approx - 0.886405, y_{2} \approx 0.886405

Show Solution