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Simplifying x2 + -40x + -150 = 0 Reorder the terms: -150 + -40x + x2 = 0 Solving -150 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '150' to each side of the equation. -150 + -40x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + -40x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + -40x + x2 = 0 + 150 -40x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 -40x + x2 = 150 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 = 150 + 400 Reorder the terms: 400 + -40x + x2 = 150 + 400 Combine like terms: 150 + 400 = 550 400 + -40x + x2 = 550 Factor a perfect square on the left side: (x + -20)(x + -20) = 550 Calculate the square root of the right side: 23.452078799 Break this problem into two subproblems by setting (x + -20) equal to 23.452078799 and -23.452078799.Subproblem 1
x + -20 = 23.452078799 Simplifying x + -20 = 23.452078799 Reorder the terms: -20 + x = 23.452078799 Solving -20 + x = 23.452078799 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 = 23.452078799 + 20 Combine like terms: -20 + 20 = 0 0 + x = 23.452078799 + 20 x = 23.452078799 + 20 Combine like terms: 23.452078799 + 20 = 43.452078799 x = 43.452078799 Simplifying x = 43.452078799Subproblem 2
x + -20 = -23.452078799 Simplifying x + -20 = -23.452078799 Reorder the terms: -20 + x = -23.452078799 Solving -20 + x = -23.452078799 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 = -23.452078799 + 20 Combine like terms: -20 + 20 = 0 0 + x = -23.452078799 + 20 x = -23.452078799 + 20 Combine like terms: -23.452078799 + 20 = -3.452078799 x = -3.452078799 Simplifying x = -3.452078799Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.452078799, -3.452078799}
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