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Simplifying x2 + 40x = -30 Reorder the terms: 40x + x2 = -30 Solving 40x + x2 = -30 Solving for variable 'x'. Reorder the terms: 30 + 40x + x2 = -30 + 30 Combine like terms: -30 + 30 = 0 30 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + 40x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + 40x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 40x + x2 = 0 + -30 40x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 40x + x2 = -30 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = -30 + 400 Reorder the terms: 400 + 40x + x2 = -30 + 400 Combine like terms: -30 + 400 = 370 400 + 40x + x2 = 370 Factor a perfect square on the left side: (x + 20)(x + 20) = 370 Calculate the square root of the right side: 19.235384062 Break this problem into two subproblems by setting (x + 20) equal to 19.235384062 and -19.235384062.Subproblem 1
x + 20 = 19.235384062 Simplifying x + 20 = 19.235384062 Reorder the terms: 20 + x = 19.235384062 Solving 20 + x = 19.235384062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 19.235384062 + -20 Combine like terms: 20 + -20 = 0 0 + x = 19.235384062 + -20 x = 19.235384062 + -20 Combine like terms: 19.235384062 + -20 = -0.764615938 x = -0.764615938 Simplifying x = -0.764615938Subproblem 2
x + 20 = -19.235384062 Simplifying x + 20 = -19.235384062 Reorder the terms: 20 + x = -19.235384062 Solving 20 + x = -19.235384062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -19.235384062 + -20 Combine like terms: 20 + -20 = 0 0 + x = -19.235384062 + -20 x = -19.235384062 + -20 Combine like terms: -19.235384062 + -20 = -39.235384062 x = -39.235384062 Simplifying x = -39.235384062Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.764615938, -39.235384062}
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