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Simplifying 4x2 + -16x + -252 = 0 Reorder the terms: -252 + -16x + 4x2 = 0 Solving -252 + -16x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-63 + -4x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-63 + -4x + x2)' equal to zero and attempt to solve: Simplifying -63 + -4x + x2 = 0 Solving -63 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + -4x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + -4x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + -4x + x2 = 0 + 63 -4x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 -4x + x2 = 63 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 63 + 4 Reorder the terms: 4 + -4x + x2 = 63 + 4 Combine like terms: 63 + 4 = 67 4 + -4x + x2 = 67 Factor a perfect square on the left side: (x + -2)(x + -2) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (x + -2) equal to 8.185352772 and -8.185352772.Subproblem 1
x + -2 = 8.185352772 Simplifying x + -2 = 8.185352772 Reorder the terms: -2 + x = 8.185352772 Solving -2 + x = 8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 8.185352772 + 2 Combine like terms: -2 + 2 = 0 0 + x = 8.185352772 + 2 x = 8.185352772 + 2 Combine like terms: 8.185352772 + 2 = 10.185352772 x = 10.185352772 Simplifying x = 10.185352772Subproblem 2
x + -2 = -8.185352772 Simplifying x + -2 = -8.185352772 Reorder the terms: -2 + x = -8.185352772 Solving -2 + x = -8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -8.185352772 + 2 Combine like terms: -2 + 2 = 0 0 + x = -8.185352772 + 2 x = -8.185352772 + 2 Combine like terms: -8.185352772 + 2 = -6.185352772 x = -6.185352772 Simplifying x = -6.185352772Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.185352772, -6.185352772}Solution
x = {10.185352772, -6.185352772}
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