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Simplifying 2x2 + 8x + -42 = 114 Reorder the terms: -42 + 8x + 2x2 = 114 Solving -42 + 8x + 2x2 = 114 Solving for variable 'x'. Reorder the terms: -42 + -114 + 8x + 2x2 = 114 + -114 Combine like terms: -42 + -114 = -156 -156 + 8x + 2x2 = 114 + -114 Combine like terms: 114 + -114 = 0 -156 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-78 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-78 + 4x + x2)' equal to zero and attempt to solve: Simplifying -78 + 4x + x2 = 0 Solving -78 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '78' to each side of the equation. -78 + 4x + 78 + x2 = 0 + 78 Reorder the terms: -78 + 78 + 4x + x2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + 4x + x2 = 0 + 78 4x + x2 = 0 + 78 Combine like terms: 0 + 78 = 78 4x + x2 = 78 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 = 78 + 4 Reorder the terms: 4 + 4x + x2 = 78 + 4 Combine like terms: 78 + 4 = 82 4 + 4x + x2 = 82 Factor a perfect square on the left side: (x + 2)(x + 2) = 82 Calculate the square root of the right side: 9.055385138 Break this problem into two subproblems by setting (x + 2) equal to 9.055385138 and -9.055385138.Subproblem 1
x + 2 = 9.055385138 Simplifying x + 2 = 9.055385138 Reorder the terms: 2 + x = 9.055385138 Solving 2 + x = 9.055385138 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 = 9.055385138 + -2 Combine like terms: 2 + -2 = 0 0 + x = 9.055385138 + -2 x = 9.055385138 + -2 Combine like terms: 9.055385138 + -2 = 7.055385138 x = 7.055385138 Simplifying x = 7.055385138Subproblem 2
x + 2 = -9.055385138 Simplifying x + 2 = -9.055385138 Reorder the terms: 2 + x = -9.055385138 Solving 2 + x = -9.055385138 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 = -9.055385138 + -2 Combine like terms: 2 + -2 = 0 0 + x = -9.055385138 + -2 x = -9.055385138 + -2 Combine like terms: -9.055385138 + -2 = -11.055385138 x = -11.055385138 Simplifying x = -11.055385138Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.055385138, -11.055385138}Solution
x = {7.055385138, -11.055385138}
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