Question

Find all real solutions of the equation by completing the square x^2 − 12 x + 30 = 43

x^1 = _____
x^2 = ______

Answer 1

• x²-12x+30=43
• x²-12x=13

Multiply by 4

• 4x²-48x=52
• (2x)²-2(2x)(12)=52
• (2x)²-2(2x)(12)+(12)²=52+144
• (2x-12)²=196
• (2x-12)=±14
• 2x=12±14
• x=6±7
• x=13,-1

Answer 2

• x = 13
• x = - 1

Explanation:

Given equation:

• x² − 12x + 30 = 43

Complete the square:

• x² - 2*6*x + 6² - 6 = 43
• (x - 6)² = 49
• (x - 6)² = 7²

1. x - 6 = 7 ⇒ x = 13
2. x - 6 = - 7 ⇒ x = - 1