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Simplifying x2 + 20x + -70 = -8 Reorder the terms: -70 + 20x + x2 = -8 Solving -70 + 20x + x2 = -8 Solving for variable 'x'. Reorder the terms: -70 + 8 + 20x + x2 = -8 + 8 Combine like terms: -70 + 8 = -62 -62 + 20x + x2 = -8 + 8 Combine like terms: -8 + 8 = 0 -62 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '62' to each side of the equation. -62 + 20x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + 20x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + 20x + x2 = 0 + 62 20x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 20x + x2 = 62 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 = 62 + 100 Reorder the terms: 100 + 20x + x2 = 62 + 100 Combine like terms: 62 + 100 = 162 100 + 20x + x2 = 162 Factor a perfect square on the left side: (x + 10)(x + 10) = 162 Calculate the square root of the right side: 12.727922061 Break this problem into two subproblems by setting (x + 10) equal to 12.727922061 and -12.727922061.Subproblem 1
x + 10 = 12.727922061 Simplifying x + 10 = 12.727922061 Reorder the terms: 10 + x = 12.727922061 Solving 10 + x = 12.727922061 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 = 12.727922061 + -10 Combine like terms: 10 + -10 = 0 0 + x = 12.727922061 + -10 x = 12.727922061 + -10 Combine like terms: 12.727922061 + -10 = 2.727922061 x = 2.727922061 Simplifying x = 2.727922061Subproblem 2
x + 10 = -12.727922061 Simplifying x + 10 = -12.727922061 Reorder the terms: 10 + x = -12.727922061 Solving 10 + x = -12.727922061 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 = -12.727922061 + -10 Combine like terms: 10 + -10 = 0 0 + x = -12.727922061 + -10 x = -12.727922061 + -10 Combine like terms: -12.727922061 + -10 = -22.727922061 x = -22.727922061 Simplifying x = -22.727922061Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.727922061, -22.727922061}
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