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Simplifying 40 = x2 + 36x + -87 Reorder the terms: 40 = -87 + 36x + x2 Solving 40 = -87 + 36x + x2 Solving for variable 'x'. Combine like terms: 40 + 87 = 127 127 + -36x + -1x2 = -87 + 36x + x2 + 87 + -36x + -1x2 Reorder the terms: 127 + -36x + -1x2 = -87 + 87 + 36x + -36x + x2 + -1x2 Combine like terms: -87 + 87 = 0 127 + -36x + -1x2 = 0 + 36x + -36x + x2 + -1x2 127 + -36x + -1x2 = 36x + -36x + x2 + -1x2 Combine like terms: 36x + -36x = 0 127 + -36x + -1x2 = 0 + x2 + -1x2 127 + -36x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 127 + -36x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -127 + 36x + x2 = 0 Move the constant term to the right: Add '127' to each side of the equation. -127 + 36x + 127 + x2 = 0 + 127 Reorder the terms: -127 + 127 + 36x + x2 = 0 + 127 Combine like terms: -127 + 127 = 0 0 + 36x + x2 = 0 + 127 36x + x2 = 0 + 127 Combine like terms: 0 + 127 = 127 36x + x2 = 127 The x term is 36x. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36x + 324 + x2 = 127 + 324 Reorder the terms: 324 + 36x + x2 = 127 + 324 Combine like terms: 127 + 324 = 451 324 + 36x + x2 = 451 Factor a perfect square on the left side: (x + 18)(x + 18) = 451 Calculate the square root of the right side: 21.236760582 Break this problem into two subproblems by setting (x + 18) equal to 21.236760582 and -21.236760582.Subproblem 1
x + 18 = 21.236760582 Simplifying x + 18 = 21.236760582 Reorder the terms: 18 + x = 21.236760582 Solving 18 + x = 21.236760582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 21.236760582 + -18 Combine like terms: 18 + -18 = 0 0 + x = 21.236760582 + -18 x = 21.236760582 + -18 Combine like terms: 21.236760582 + -18 = 3.236760582 x = 3.236760582 Simplifying x = 3.236760582Subproblem 2
x + 18 = -21.236760582 Simplifying x + 18 = -21.236760582 Reorder the terms: 18 + x = -21.236760582 Solving 18 + x = -21.236760582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -21.236760582 + -18 Combine like terms: 18 + -18 = 0 0 + x = -21.236760582 + -18 x = -21.236760582 + -18 Combine like terms: -21.236760582 + -18 = -39.236760582 x = -39.236760582 Simplifying x = -39.236760582Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.236760582, -39.236760582}
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