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Simplifying 2x2 = 36x + 64 Reorder the terms: 2x2 = 64 + 36x Solving 2x2 = 64 + 36x Solving for variable 'x'. Reorder the terms: -64 + -36x + 2x2 = 64 + 36x + -64 + -36x Reorder the terms: -64 + -36x + 2x2 = 64 + -64 + 36x + -36x Combine like terms: 64 + -64 = 0 -64 + -36x + 2x2 = 0 + 36x + -36x -64 + -36x + 2x2 = 36x + -36x Combine like terms: 36x + -36x = 0 -64 + -36x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-32 + -18x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-32 + -18x + x2)' equal to zero and attempt to solve: Simplifying -32 + -18x + x2 = 0 Solving -32 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -18x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -18x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -18x + x2 = 0 + 32 -18x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -18x + x2 = 32 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 32 + 81 Reorder the terms: 81 + -18x + x2 = 32 + 81 Combine like terms: 32 + 81 = 113 81 + -18x + x2 = 113 Factor a perfect square on the left side: (x + -9)(x + -9) = 113 Calculate the square root of the right side: 10.630145813 Break this problem into two subproblems by setting (x + -9) equal to 10.630145813 and -10.630145813.Subproblem 1
x + -9 = 10.630145813 Simplifying x + -9 = 10.630145813 Reorder the terms: -9 + x = 10.630145813 Solving -9 + x = 10.630145813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 10.630145813 + 9 Combine like terms: -9 + 9 = 0 0 + x = 10.630145813 + 9 x = 10.630145813 + 9 Combine like terms: 10.630145813 + 9 = 19.630145813 x = 19.630145813 Simplifying x = 19.630145813Subproblem 2
x + -9 = -10.630145813 Simplifying x + -9 = -10.630145813 Reorder the terms: -9 + x = -10.630145813 Solving -9 + x = -10.630145813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -10.630145813 + 9 Combine like terms: -9 + 9 = 0 0 + x = -10.630145813 + 9 x = -10.630145813 + 9 Combine like terms: -10.630145813 + 9 = -1.630145813 x = -1.630145813 Simplifying x = -1.630145813Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.630145813, -1.630145813}Solution
x = {19.630145813, -1.630145813}
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