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Simplifying 2x2 + 52x + 62 = 0 Reorder the terms: 62 + 52x + 2x2 = 0 Solving 62 + 52x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(31 + 26x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(31 + 26x + x2)' equal to zero and attempt to solve: Simplifying 31 + 26x + x2 = 0 Solving 31 + 26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + 26x + -31 + x2 = 0 + -31 Reorder the terms: 31 + -31 + 26x + x2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 26x + x2 = 0 + -31 26x + x2 = 0 + -31 Combine like terms: 0 + -31 = -31 26x + x2 = -31 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = -31 + 169 Reorder the terms: 169 + 26x + x2 = -31 + 169 Combine like terms: -31 + 169 = 138 169 + 26x + x2 = 138 Factor a perfect square on the left side: (x + 13)(x + 13) = 138 Calculate the square root of the right side: 11.747340124 Break this problem into two subproblems by setting (x + 13) equal to 11.747340124 and -11.747340124.Subproblem 1
x + 13 = 11.747340124 Simplifying x + 13 = 11.747340124 Reorder the terms: 13 + x = 11.747340124 Solving 13 + x = 11.747340124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 11.747340124 + -13 Combine like terms: 13 + -13 = 0 0 + x = 11.747340124 + -13 x = 11.747340124 + -13 Combine like terms: 11.747340124 + -13 = -1.252659876 x = -1.252659876 Simplifying x = -1.252659876Subproblem 2
x + 13 = -11.747340124 Simplifying x + 13 = -11.747340124 Reorder the terms: 13 + x = -11.747340124 Solving 13 + x = -11.747340124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -11.747340124 + -13 Combine like terms: 13 + -13 = 0 0 + x = -11.747340124 + -13 x = -11.747340124 + -13 Combine like terms: -11.747340124 + -13 = -24.747340124 x = -24.747340124 Simplifying x = -24.747340124Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.252659876, -24.747340124}Solution
x = {-1.252659876, -24.747340124}
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