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Simplifying x2 + 40x = -357 Reorder the terms: 40x + x2 = -357 Solving 40x + x2 = -357 Solving for variable 'x'. Reorder the terms: 357 + 40x + x2 = -357 + 357 Combine like terms: -357 + 357 = 0 357 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-357' to each side of the equation. 357 + 40x + -357 + x2 = 0 + -357 Reorder the terms: 357 + -357 + 40x + x2 = 0 + -357 Combine like terms: 357 + -357 = 0 0 + 40x + x2 = 0 + -357 40x + x2 = 0 + -357 Combine like terms: 0 + -357 = -357 40x + x2 = -357 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 = -357 + 400 Reorder the terms: 400 + 40x + x2 = -357 + 400 Combine like terms: -357 + 400 = 43 400 + 40x + x2 = 43 Factor a perfect square on the left side: (x + 20)(x + 20) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (x + 20) equal to 6.557438524 and -6.557438524.Subproblem 1
x + 20 = 6.557438524 Simplifying x + 20 = 6.557438524 Reorder the terms: 20 + x = 6.557438524 Solving 20 + x = 6.557438524 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 = 6.557438524 + -20 Combine like terms: 20 + -20 = 0 0 + x = 6.557438524 + -20 x = 6.557438524 + -20 Combine like terms: 6.557438524 + -20 = -13.442561476 x = -13.442561476 Simplifying x = -13.442561476Subproblem 2
x + 20 = -6.557438524 Simplifying x + 20 = -6.557438524 Reorder the terms: 20 + x = -6.557438524 Solving 20 + x = -6.557438524 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 = -6.557438524 + -20 Combine like terms: 20 + -20 = 0 0 + x = -6.557438524 + -20 x = -6.557438524 + -20 Combine like terms: -6.557438524 + -20 = -26.557438524 x = -26.557438524 Simplifying x = -26.557438524Solution
The solution to the problem is based on the solutions from the subproblems. x = {-13.442561476, -26.557438524}
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