Solve y^2 -12y - 84

Question

Find the roots

y_{1} = 6 - 230, y_{2} = 6 + 230

Alternative Form

y_{1} \approx - 4.954451, y_{2} \approx 16.954451

Evaluate

y^{2} - 12 y - 84

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

y^{2} - 12 y - 84 = 0

Substitute a= 1,b= - 12 and c= - 84 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{12 \pm ( - 12 ) ^{2} - 4 ( - 84 )}{2}

Simplify the expression

More Steps

Evaluate

(- 12)^{2} - 4 (- 84)

Multiply the numbers

More Steps

Evaluate

4 (- 84)

Multiplying or dividing an odd number of negative terms equals a negative

- 4 \times 84

Multiply the numbers

- 336

(- 12)^{2} - (- 336)

Rewrite the expression

1 2^{2} - (- 336)

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

1 2^{2} + 336

Evaluate the power

144 + 336

Add the numbers

480

y = \frac{12 \pm 480}{2}

Simplify the radical expression

More Steps

Evaluate

480

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

16 \times 30

Write the number in exponential form with the base of 4

4^{2} \times 30

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

4^{2} \times 30

Reduce the index of the radical and exponent with 2

430

y = \frac{12 \pm 4 30}{2}

Separate the equation into 2 possible cases

y = \frac{12 + 4 30}{2} y = \frac{12 - 4 30}{2}

Simplify the expression

More Steps

Evaluate

y = \frac{12 + 4 30}{2}

Divide the terms

More Steps

Evaluate

\frac{12 + 4 30}{2}

Rewrite the expression

\frac{2 ( 6 + 2 30 )}{2}

Reduce the fraction

6 + 230

y = 6 + 230

y = 6 + 230 y = \frac{12 - 4 30}{2}

Simplify the expression

More Steps

Evaluate

y = \frac{12 - 4 30}{2}

Divide the terms

More Steps

Evaluate

\frac{12 - 4 30}{2}

Rewrite the expression

\frac{2 ( 6 - 2 30 )}{2}

Reduce the fraction

6 - 230

y = 6 - 230

y = 6 + 230 y = 6 - 230

Solution

y_{1} = 6 - 230, y_{2} = 6 + 230

Alternative Form

y_{1} \approx - 4.954451, y_{2} \approx 16.954451

Show Solution