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Simplifying x2 + 20x = -2 Reorder the terms: 20x + x2 = -2 Solving 20x + x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + 20x + x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 20x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 20x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 20x + x2 = 0 + -2 20x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 20x + x2 = -2 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 = -2 + 100 Reorder the terms: 100 + 20x + x2 = -2 + 100 Combine like terms: -2 + 100 = 98 100 + 20x + x2 = 98 Factor a perfect square on the left side: (x + 10)(x + 10) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (x + 10) equal to 9.899494937 and -9.899494937.Subproblem 1
x + 10 = 9.899494937 Simplifying x + 10 = 9.899494937 Reorder the terms: 10 + x = 9.899494937 Solving 10 + x = 9.899494937 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 = 9.899494937 + -10 Combine like terms: 10 + -10 = 0 0 + x = 9.899494937 + -10 x = 9.899494937 + -10 Combine like terms: 9.899494937 + -10 = -0.100505063 x = -0.100505063 Simplifying x = -0.100505063Subproblem 2
x + 10 = -9.899494937 Simplifying x + 10 = -9.899494937 Reorder the terms: 10 + x = -9.899494937 Solving 10 + x = -9.899494937 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 = -9.899494937 + -10 Combine like terms: 10 + -10 = 0 0 + x = -9.899494937 + -10 x = -9.899494937 + -10 Combine like terms: -9.899494937 + -10 = -19.899494937 x = -19.899494937 Simplifying x = -19.899494937Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.100505063, -19.899494937}
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