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Simplifying x2 + 12x = 90 Reorder the terms: 12x + x2 = 90 Solving 12x + x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + 12x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 12x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 12x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 12x + x2 = 0 + 90 12x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 12x + x2 = 90 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 90 + 36 Reorder the terms: 36 + 12x + x2 = 90 + 36 Combine like terms: 90 + 36 = 126 36 + 12x + x2 = 126 Factor a perfect square on the left side: (x + 6)(x + 6) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (x + 6) equal to 11.22497216 and -11.22497216.Subproblem 1
x + 6 = 11.22497216 Simplifying x + 6 = 11.22497216 Reorder the terms: 6 + x = 11.22497216 Solving 6 + x = 11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 11.22497216 + -6 Combine like terms: 6 + -6 = 0 0 + x = 11.22497216 + -6 x = 11.22497216 + -6 Combine like terms: 11.22497216 + -6 = 5.22497216 x = 5.22497216 Simplifying x = 5.22497216Subproblem 2
x + 6 = -11.22497216 Simplifying x + 6 = -11.22497216 Reorder the terms: 6 + x = -11.22497216 Solving 6 + x = -11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -11.22497216 + -6 Combine like terms: 6 + -6 = 0 0 + x = -11.22497216 + -6 x = -11.22497216 + -6 Combine like terms: -11.22497216 + -6 = -17.22497216 x = -17.22497216 Simplifying x = -17.22497216Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.22497216, -17.22497216}
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