Question

Solve by completing the square.

y² + 30y = -7
Write your answers as integers, proper or improper fractions in simplest form, or decimals
rounded to the nearest hundredth.
y =
Submit
or y =

Answer 1

Answers:

y = ± 221.47, y = -0.24, y = -29.76

Explanation:

y^2 + 30y = -7

Move -7 over to the other side

y^2 + 30y +7 = 0

This takes form of a quadratic equation of ax^2 + bx + c = 0, where y = x

Quadratic formula is x = (-b ± (sqrtb^2 - 4ac)/2a and replace everything so it's y = (-30 ± (sqrt30^2 - 4*1*7)/2*1. Once solved, the answer choices are y = ± 221.47, y = -0.24, or -29.76.

Answer 2

• y = 0.24 or y = - 29.76

==============================

Identity of the square of a sum of two numbers:

• (a + b)² = a² + 2ab + b²

Given equation:

• y² + 30y = - 7

We can see one of the numbers is y, and the second one is 15 as twice the product is 30y.

Add 15² = 225 to both sides to complete the square, then solve it:

• y² + 2*15y + 15² = 225 - 7
• (y + 15)² = 218
• y + 15 = ± √218
• y = - 15 ± √218
• y = - 15 ± 14.76 (rounded to the nearest hundredths)
• y = 0.24 or y = - 29.76