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Simplifying x2 + 40x + -1500 = 0 Reorder the terms: -1500 + 40x + x2 = 0 Solving -1500 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1500' to each side of the equation. -1500 + 40x + 1500 + x2 = 0 + 1500 Reorder the terms: -1500 + 1500 + 40x + x2 = 0 + 1500 Combine like terms: -1500 + 1500 = 0 0 + 40x + x2 = 0 + 1500 40x + x2 = 0 + 1500 Combine like terms: 0 + 1500 = 1500 40x + x2 = 1500 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 = 1500 + 400 Reorder the terms: 400 + 40x + x2 = 1500 + 400 Combine like terms: 1500 + 400 = 1900 400 + 40x + x2 = 1900 Factor a perfect square on the left side: (x + 20)(x + 20) = 1900 Calculate the square root of the right side: 43.588989435 Break this problem into two subproblems by setting (x + 20) equal to 43.588989435 and -43.588989435.Subproblem 1
x + 20 = 43.588989435 Simplifying x + 20 = 43.588989435 Reorder the terms: 20 + x = 43.588989435 Solving 20 + x = 43.588989435 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 = 43.588989435 + -20 Combine like terms: 20 + -20 = 0 0 + x = 43.588989435 + -20 x = 43.588989435 + -20 Combine like terms: 43.588989435 + -20 = 23.588989435 x = 23.588989435 Simplifying x = 23.588989435Subproblem 2
x + 20 = -43.588989435 Simplifying x + 20 = -43.588989435 Reorder the terms: 20 + x = -43.588989435 Solving 20 + x = -43.588989435 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 = -43.588989435 + -20 Combine like terms: 20 + -20 = 0 0 + x = -43.588989435 + -20 x = -43.588989435 + -20 Combine like terms: -43.588989435 + -20 = -63.588989435 x = -63.588989435 Simplifying x = -63.588989435Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.588989435, -63.588989435}
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