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Simplifying 2(x2 + -8x + -480) = 0 Reorder the terms: 2(-480 + -8x + x2) = 0 (-480 * 2 + -8x * 2 + x2 * 2) = 0 (-960 + -16x + 2x2) = 0 Solving -960 + -16x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-480 + -8x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-480 + -8x + x2)' equal to zero and attempt to solve: Simplifying -480 + -8x + x2 = 0 Solving -480 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '480' to each side of the equation. -480 + -8x + 480 + x2 = 0 + 480 Reorder the terms: -480 + 480 + -8x + x2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + -8x + x2 = 0 + 480 -8x + x2 = 0 + 480 Combine like terms: 0 + 480 = 480 -8x + x2 = 480 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 = 480 + 16 Reorder the terms: 16 + -8x + x2 = 480 + 16 Combine like terms: 480 + 16 = 496 16 + -8x + x2 = 496 Factor a perfect square on the left side: (x + -4)(x + -4) = 496 Calculate the square root of the right side: 22.271057451 Break this problem into two subproblems by setting (x + -4) equal to 22.271057451 and -22.271057451.Subproblem 1
x + -4 = 22.271057451 Simplifying x + -4 = 22.271057451 Reorder the terms: -4 + x = 22.271057451 Solving -4 + x = 22.271057451 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 = 22.271057451 + 4 Combine like terms: -4 + 4 = 0 0 + x = 22.271057451 + 4 x = 22.271057451 + 4 Combine like terms: 22.271057451 + 4 = 26.271057451 x = 26.271057451 Simplifying x = 26.271057451Subproblem 2
x + -4 = -22.271057451 Simplifying x + -4 = -22.271057451 Reorder the terms: -4 + x = -22.271057451 Solving -4 + x = -22.271057451 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 = -22.271057451 + 4 Combine like terms: -4 + 4 = 0 0 + x = -22.271057451 + 4 x = -22.271057451 + 4 Combine like terms: -22.271057451 + 4 = -18.271057451 x = -18.271057451 Simplifying x = -18.271057451Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.271057451, -18.271057451}Solution
x = {26.271057451, -18.271057451}
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