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Simplifying x2 + 20x + -142 = 0 Reorder the terms: -142 + 20x + x2 = 0 Solving -142 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '142' to each side of the equation. -142 + 20x + 142 + x2 = 0 + 142 Reorder the terms: -142 + 142 + 20x + x2 = 0 + 142 Combine like terms: -142 + 142 = 0 0 + 20x + x2 = 0 + 142 20x + x2 = 0 + 142 Combine like terms: 0 + 142 = 142 20x + x2 = 142 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 = 142 + 100 Reorder the terms: 100 + 20x + x2 = 142 + 100 Combine like terms: 142 + 100 = 242 100 + 20x + x2 = 242 Factor a perfect square on the left side: (x + 10)(x + 10) = 242 Calculate the square root of the right side: 15.556349186 Break this problem into two subproblems by setting (x + 10) equal to 15.556349186 and -15.556349186.Subproblem 1
x + 10 = 15.556349186 Simplifying x + 10 = 15.556349186 Reorder the terms: 10 + x = 15.556349186 Solving 10 + x = 15.556349186 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 = 15.556349186 + -10 Combine like terms: 10 + -10 = 0 0 + x = 15.556349186 + -10 x = 15.556349186 + -10 Combine like terms: 15.556349186 + -10 = 5.556349186 x = 5.556349186 Simplifying x = 5.556349186Subproblem 2
x + 10 = -15.556349186 Simplifying x + 10 = -15.556349186 Reorder the terms: 10 + x = -15.556349186 Solving 10 + x = -15.556349186 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 = -15.556349186 + -10 Combine like terms: 10 + -10 = 0 0 + x = -15.556349186 + -10 x = -15.556349186 + -10 Combine like terms: -15.556349186 + -10 = -25.556349186 x = -25.556349186 Simplifying x = -25.556349186Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.556349186, -25.556349186}
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