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Simplifying (x)(2x + -4) = 224 Reorder the terms: x(-4 + 2x) = 224 (-4 * x + 2x * x) = 224 (-4x + 2x2) = 224 Solving -4x + 2x2 = 224 Solving for variable 'x'. Reorder the terms: -224 + -4x + 2x2 = 224 + -224 Combine like terms: 224 + -224 = 0 -224 + -4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-112 + -2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-112 + -2x + x2)' equal to zero and attempt to solve: Simplifying -112 + -2x + x2 = 0 Solving -112 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '112' to each side of the equation. -112 + -2x + 112 + x2 = 0 + 112 Reorder the terms: -112 + 112 + -2x + x2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + -2x + x2 = 0 + 112 -2x + x2 = 0 + 112 Combine like terms: 0 + 112 = 112 -2x + x2 = 112 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 112 + 1 Reorder the terms: 1 + -2x + x2 = 112 + 1 Combine like terms: 112 + 1 = 113 1 + -2x + x2 = 113 Factor a perfect square on the left side: (x + -1)(x + -1) = 113 Calculate the square root of the right side: 10.630145813 Break this problem into two subproblems by setting (x + -1) equal to 10.630145813 and -10.630145813.Subproblem 1
x + -1 = 10.630145813 Simplifying x + -1 = 10.630145813 Reorder the terms: -1 + x = 10.630145813 Solving -1 + x = 10.630145813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 10.630145813 + 1 Combine like terms: -1 + 1 = 0 0 + x = 10.630145813 + 1 x = 10.630145813 + 1 Combine like terms: 10.630145813 + 1 = 11.630145813 x = 11.630145813 Simplifying x = 11.630145813Subproblem 2
x + -1 = -10.630145813 Simplifying x + -1 = -10.630145813 Reorder the terms: -1 + x = -10.630145813 Solving -1 + x = -10.630145813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -10.630145813 + 1 Combine like terms: -1 + 1 = 0 0 + x = -10.630145813 + 1 x = -10.630145813 + 1 Combine like terms: -10.630145813 + 1 = -9.630145813 x = -9.630145813 Simplifying x = -9.630145813Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.630145813, -9.630145813}Solution
x = {11.630145813, -9.630145813}
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