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Simplifying x2 = 32x + 240 Reorder the terms: x2 = 240 + 32x Solving x2 = 240 + 32x Solving for variable 'x'. Reorder the terms: -240 + -32x + x2 = 240 + 32x + -240 + -32x Reorder the terms: -240 + -32x + x2 = 240 + -240 + 32x + -32x Combine like terms: 240 + -240 = 0 -240 + -32x + x2 = 0 + 32x + -32x -240 + -32x + x2 = 32x + -32x Combine like terms: 32x + -32x = 0 -240 + -32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + -32x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + -32x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + -32x + x2 = 0 + 240 -32x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 -32x + x2 = 240 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = 240 + 256 Reorder the terms: 256 + -32x + x2 = 240 + 256 Combine like terms: 240 + 256 = 496 256 + -32x + x2 = 496 Factor a perfect square on the left side: (x + -16)(x + -16) = 496 Calculate the square root of the right side: 22.271057451 Break this problem into two subproblems by setting (x + -16) equal to 22.271057451 and -22.271057451.Subproblem 1
x + -16 = 22.271057451 Simplifying x + -16 = 22.271057451 Reorder the terms: -16 + x = 22.271057451 Solving -16 + x = 22.271057451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 22.271057451 + 16 Combine like terms: -16 + 16 = 0 0 + x = 22.271057451 + 16 x = 22.271057451 + 16 Combine like terms: 22.271057451 + 16 = 38.271057451 x = 38.271057451 Simplifying x = 38.271057451Subproblem 2
x + -16 = -22.271057451 Simplifying x + -16 = -22.271057451 Reorder the terms: -16 + x = -22.271057451 Solving -16 + x = -22.271057451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -22.271057451 + 16 Combine like terms: -16 + 16 = 0 0 + x = -22.271057451 + 16 x = -22.271057451 + 16 Combine like terms: -22.271057451 + 16 = -6.271057451 x = -6.271057451 Simplifying x = -6.271057451Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.271057451, -6.271057451}
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