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Simplifying x(x + 1) + (x + 2) = 90 Reorder the terms: x(1 + x) + (x + 2) = 90 (1 * x + x * x) + (x + 2) = 90 (1x + x2) + (x + 2) = 90 Reorder the terms: 1x + x2 + (2 + x) = 90 Remove parenthesis around (2 + x) 1x + x2 + 2 + x = 90 Reorder the terms: 2 + 1x + x + x2 = 90 Combine like terms: 1x + x = 2x 2 + 2x + x2 = 90 Solving 2 + 2x + x2 = 90 Solving for variable 'x'. Reorder the terms: 2 + -90 + 2x + x2 = 90 + -90 Combine like terms: 2 + -90 = -88 -88 + 2x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -88 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + 2x + 88 + x2 = 0 + 88 Reorder the terms: -88 + 88 + 2x + x2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + 2x + x2 = 0 + 88 2x + x2 = 0 + 88 Combine like terms: 0 + 88 = 88 2x + x2 = 88 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 88 + 1 Reorder the terms: 1 + 2x + x2 = 88 + 1 Combine like terms: 88 + 1 = 89 1 + 2x + x2 = 89 Factor a perfect square on the left side: (x + 1)(x + 1) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (x + 1) equal to 9.433981132 and -9.433981132.Subproblem 1
x + 1 = 9.433981132 Simplifying x + 1 = 9.433981132 Reorder the terms: 1 + x = 9.433981132 Solving 1 + x = 9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 9.433981132 + -1 Combine like terms: 1 + -1 = 0 0 + x = 9.433981132 + -1 x = 9.433981132 + -1 Combine like terms: 9.433981132 + -1 = 8.433981132 x = 8.433981132 Simplifying x = 8.433981132Subproblem 2
x + 1 = -9.433981132 Simplifying x + 1 = -9.433981132 Reorder the terms: 1 + x = -9.433981132 Solving 1 + x = -9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -9.433981132 + -1 Combine like terms: 1 + -1 = 0 0 + x = -9.433981132 + -1 x = -9.433981132 + -1 Combine like terms: -9.433981132 + -1 = -10.433981132 x = -10.433981132 Simplifying x = -10.433981132Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.433981132, -10.433981132}
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