Question

(x+2)²=(x-6)² Help me pls

Answer 1

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Answer 2

x^2+4x+4=x^2-12x+36 (відкриваємо душки )

скорочуємо x^2

4x+4= -12x+36

4x+4+12x-36=0

16x+4-36=0

16x-32=0

скорочуємо обидві сторони рівняння на 16

x-2=0

x=2

Answer 3

Sure, let's solve the equation step by step.

Given equation: (x+2)² = (x-6)²

Step 1: Expand both sides of the equation using the formula for squaring a binomial: (x+2)² = x² + 2x2 + 2² (x-6)² = x² - 2x6 + 6²

Step 2: Simplify both sides: x² + 4x + 4 = x² - 12x + 36

Step 3: Move all the terms to one side of the equation to get it in standard form: x² - x² + 4x + 12x + 4 - 36 = 0

Step 4: Combine like terms: 16x - 32 = 0

Step 5: Add 32 to both sides of the equation: 16x = 32

Step 6: Divide both sides by 16 to isolate x: x = 32 / 16

Step 7: Simplify: x = 2

So, the solution to the equation (x+2)² = (x-6)² is x = 2.