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Simplifying 2x2 + -16x + -76 = 0 Reorder the terms: -76 + -16x + 2x2 = 0 Solving -76 + -16x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-38 + -8x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-38 + -8x + x2)' equal to zero and attempt to solve: Simplifying -38 + -8x + x2 = 0 Solving -38 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + -8x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + -8x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + -8x + x2 = 0 + 38 -8x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 -8x + x2 = 38 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 = 38 + 16 Reorder the terms: 16 + -8x + x2 = 38 + 16 Combine like terms: 38 + 16 = 54 16 + -8x + x2 = 54 Factor a perfect square on the left side: (x + -4)(x + -4) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (x + -4) equal to 7.348469228 and -7.348469228.Subproblem 1
x + -4 = 7.348469228 Simplifying x + -4 = 7.348469228 Reorder the terms: -4 + x = 7.348469228 Solving -4 + x = 7.348469228 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 = 7.348469228 + 4 Combine like terms: -4 + 4 = 0 0 + x = 7.348469228 + 4 x = 7.348469228 + 4 Combine like terms: 7.348469228 + 4 = 11.348469228 x = 11.348469228 Simplifying x = 11.348469228Subproblem 2
x + -4 = -7.348469228 Simplifying x + -4 = -7.348469228 Reorder the terms: -4 + x = -7.348469228 Solving -4 + x = -7.348469228 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 = -7.348469228 + 4 Combine like terms: -4 + 4 = 0 0 + x = -7.348469228 + 4 x = -7.348469228 + 4 Combine like terms: -7.348469228 + 4 = -3.348469228 x = -3.348469228 Simplifying x = -3.348469228Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.348469228, -3.348469228}Solution
x = {11.348469228, -3.348469228}
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