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Simplifying x2 + -20x = -8 Reorder the terms: -20x + x2 = -8 Solving -20x + x2 = -8 Solving for variable 'x'. Reorder the terms: 8 + -20x + x2 = -8 + 8 Combine like terms: -8 + 8 = 0 8 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -20x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -20x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -20x + x2 = 0 + -8 -20x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -20x + x2 = -8 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 = -8 + 100 Reorder the terms: 100 + -20x + x2 = -8 + 100 Combine like terms: -8 + 100 = 92 100 + -20x + x2 = 92 Factor a perfect square on the left side: (x + -10)(x + -10) = 92 Calculate the square root of the right side: 9.591663047 Break this problem into two subproblems by setting (x + -10) equal to 9.591663047 and -9.591663047.Subproblem 1
x + -10 = 9.591663047 Simplifying x + -10 = 9.591663047 Reorder the terms: -10 + x = 9.591663047 Solving -10 + x = 9.591663047 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 = 9.591663047 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.591663047 + 10 x = 9.591663047 + 10 Combine like terms: 9.591663047 + 10 = 19.591663047 x = 19.591663047 Simplifying x = 19.591663047Subproblem 2
x + -10 = -9.591663047 Simplifying x + -10 = -9.591663047 Reorder the terms: -10 + x = -9.591663047 Solving -10 + x = -9.591663047 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 = -9.591663047 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.591663047 + 10 x = -9.591663047 + 10 Combine like terms: -9.591663047 + 10 = 0.408336953 x = 0.408336953 Simplifying x = 0.408336953Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.591663047, 0.408336953}
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