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Simplifying (x + -4)(x + -4) = 486 Reorder the terms: (-4 + x)(x + -4) = 486 Reorder the terms: (-4 + x)(-4 + x) = 486 Multiply (-4 + x) * (-4 + x) (-4(-4 + x) + x(-4 + x)) = 486 ((-4 * -4 + x * -4) + x(-4 + x)) = 486 ((16 + -4x) + x(-4 + x)) = 486 (16 + -4x + (-4 * x + x * x)) = 486 (16 + -4x + (-4x + x2)) = 486 Combine like terms: -4x + -4x = -8x (16 + -8x + x2) = 486 Solving 16 + -8x + x2 = 486 Solving for variable 'x'. Reorder the terms: 16 + -486 + -8x + x2 = 486 + -486 Combine like terms: 16 + -486 = -470 -470 + -8x + x2 = 486 + -486 Combine like terms: 486 + -486 = 0 -470 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '470' to each side of the equation. -470 + -8x + 470 + x2 = 0 + 470 Reorder the terms: -470 + 470 + -8x + x2 = 0 + 470 Combine like terms: -470 + 470 = 0 0 + -8x + x2 = 0 + 470 -8x + x2 = 0 + 470 Combine like terms: 0 + 470 = 470 -8x + x2 = 470 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 470 + 16 Reorder the terms: 16 + -8x + x2 = 470 + 16 Combine like terms: 470 + 16 = 486 16 + -8x + x2 = 486 Factor a perfect square on the left side: (x + -4)(x + -4) = 486 Calculate the square root of the right side: 22.045407685 Break this problem into two subproblems by setting (x + -4) equal to 22.045407685 and -22.045407685.Subproblem 1
x + -4 = 22.045407685 Simplifying x + -4 = 22.045407685 Reorder the terms: -4 + x = 22.045407685 Solving -4 + x = 22.045407685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 22.045407685 + 4 Combine like terms: -4 + 4 = 0 0 + x = 22.045407685 + 4 x = 22.045407685 + 4 Combine like terms: 22.045407685 + 4 = 26.045407685 x = 26.045407685 Simplifying x = 26.045407685Subproblem 2
x + -4 = -22.045407685 Simplifying x + -4 = -22.045407685 Reorder the terms: -4 + x = -22.045407685 Solving -4 + x = -22.045407685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -22.045407685 + 4 Combine like terms: -4 + 4 = 0 0 + x = -22.045407685 + 4 x = -22.045407685 + 4 Combine like terms: -22.045407685 + 4 = -18.045407685 x = -18.045407685 Simplifying x = -18.045407685Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.045407685, -18.045407685}
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