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Simplifying 2x2 + 16x + -24 = 936 Reorder the terms: -24 + 16x + 2x2 = 936 Solving -24 + 16x + 2x2 = 936 Solving for variable 'x'. Reorder the terms: -24 + -936 + 16x + 2x2 = 936 + -936 Combine like terms: -24 + -936 = -960 -960 + 16x + 2x2 = 936 + -936 Combine like terms: 936 + -936 = 0 -960 + 16x + 2x2 = 0 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 = 18.271057451 x = 18.271057451 Simplifying x = 18.271057451Subproblem 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 = -26.271057451 x = -26.271057451 Simplifying x = -26.271057451Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.271057451, -26.271057451}Solution
x = {18.271057451, -26.271057451}
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