Solve y^(2)-32y-30

Question

Find the roots

y_{1} = 16 - 286, y_{2} = 16 + 286

Alternative Form

y_{1} \approx - 0.911535, y_{2} \approx 32.911535

Evaluate

y^{2} - 32 y - 30

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

y^{2} - 32 y - 30 = 0

Substitute a= 1,b= - 32 and c= - 30 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{32 \pm ( - 32 ) ^{2} - 4 ( - 30 )}{2}

Simplify the expression

More Steps

Evaluate

(- 32)^{2} - 4 (- 30)

Multiply the numbers

More Steps

Evaluate

4 (- 30)

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

- 4 \times 30

Multiply the numbers

- 120

(- 32)^{2} - (- 120)

Rewrite the expression

3 2^{2} - (- 120)

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

3 2^{2} + 120

Evaluate the power

1024 + 120

Add the numbers

1144

y = \frac{32 \pm 1144}{2}

Simplify the radical expression

More Steps

Evaluate

1144

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

4 \times 286

Write the number in exponential form with the base of 2

2^{2} \times 286

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

2^{2} \times 286

Reduce the index of the radical and exponent with 2

2286

y = \frac{32 \pm 2 286}{2}

Separate the equation into 2 possible cases

y = \frac{32 + 2 286}{2} y = \frac{32 - 2 286}{2}

Simplify the expression

More Steps

Evaluate

y = \frac{32 + 2 286}{2}

Divide the terms

More Steps

Evaluate

\frac{32 + 2 286}{2}

Rewrite the expression

\frac{2 ( 16 + 286 )}{2}

Reduce the fraction

16 + 286

y = 16 + 286

y = 16 + 286 y = \frac{32 - 2 286}{2}

Simplify the expression

More Steps

Evaluate

y = \frac{32 - 2 286}{2}

Divide the terms

More Steps

Evaluate

\frac{32 - 2 286}{2}

Rewrite the expression

\frac{2 ( 16 - 286 )}{2}

Reduce the fraction

16 - 286

y = 16 - 286

y = 16 + 286 y = 16 - 286

Solution

y_{1} = 16 - 286, y_{2} = 16 + 286

Alternative Form

y_{1} \approx - 0.911535, y_{2} \approx 32.911535

Show Solution