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Simplifying x2 + 20x + -46 = -8 Reorder the terms: -46 + 20x + x2 = -8 Solving -46 + 20x + x2 = -8 Solving for variable 'x'. Reorder the terms: -46 + 8 + 20x + x2 = -8 + 8 Combine like terms: -46 + 8 = -38 -38 + 20x + x2 = -8 + 8 Combine like terms: -8 + 8 = 0 -38 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + 20x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + 20x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 20x + x2 = 0 + 38 20x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 20x + x2 = 38 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 38 + 100 Reorder the terms: 100 + 20x + x2 = 38 + 100 Combine like terms: 38 + 100 = 138 100 + 20x + x2 = 138 Factor a perfect square on the left side: (x + 10)(x + 10) = 138 Calculate the square root of the right side: 11.747340124 Break this problem into two subproblems by setting (x + 10) equal to 11.747340124 and -11.747340124.Subproblem 1
x + 10 = 11.747340124 Simplifying x + 10 = 11.747340124 Reorder the terms: 10 + x = 11.747340124 Solving 10 + x = 11.747340124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 11.747340124 + -10 Combine like terms: 10 + -10 = 0 0 + x = 11.747340124 + -10 x = 11.747340124 + -10 Combine like terms: 11.747340124 + -10 = 1.747340124 x = 1.747340124 Simplifying x = 1.747340124Subproblem 2
x + 10 = -11.747340124 Simplifying x + 10 = -11.747340124 Reorder the terms: 10 + x = -11.747340124 Solving 10 + x = -11.747340124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -11.747340124 + -10 Combine like terms: 10 + -10 = 0 0 + x = -11.747340124 + -10 x = -11.747340124 + -10 Combine like terms: -11.747340124 + -10 = -21.747340124 x = -21.747340124 Simplifying x = -21.747340124Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.747340124, -21.747340124}
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