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Simplifying 91 = (x + 1)(x + 2) Reorder the terms: 91 = (1 + x)(x + 2) Reorder the terms: 91 = (1 + x)(2 + x) Multiply (1 + x) * (2 + x) 91 = (1(2 + x) + x(2 + x)) 91 = ((2 * 1 + x * 1) + x(2 + x)) 91 = ((2 + 1x) + x(2 + x)) 91 = (2 + 1x + (2 * x + x * x)) 91 = (2 + 1x + (2x + x2)) Combine like terms: 1x + 2x = 3x 91 = (2 + 3x + x2) Solving 91 = 2 + 3x + x2 Solving for variable 'x'. Combine like terms: 91 + -2 = 89 89 + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2 Reorder the terms: 89 + -3x + -1x2 = 2 + -2 + 3x + -3x + x2 + -1x2 Combine like terms: 2 + -2 = 0 89 + -3x + -1x2 = 0 + 3x + -3x + x2 + -1x2 89 + -3x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 89 + -3x + -1x2 = 0 + x2 + -1x2 89 + -3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 89 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -89 + 3x + x2 = 0 Move the constant term to the right: Add '89' to each side of the equation. -89 + 3x + 89 + x2 = 0 + 89 Reorder the terms: -89 + 89 + 3x + x2 = 0 + 89 Combine like terms: -89 + 89 = 0 0 + 3x + x2 = 0 + 89 3x + x2 = 0 + 89 Combine like terms: 0 + 89 = 89 3x + x2 = 89 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 89 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 89 + 2.25 Combine like terms: 89 + 2.25 = 91.25 2.25 + 3x + x2 = 91.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 91.25 Calculate the square root of the right side: 9.552486587 Break this problem into two subproblems by setting (x + 1.5) equal to 9.552486587 and -9.552486587.Subproblem 1
x + 1.5 = 9.552486587 Simplifying x + 1.5 = 9.552486587 Reorder the terms: 1.5 + x = 9.552486587 Solving 1.5 + x = 9.552486587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 9.552486587 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 9.552486587 + -1.5 x = 9.552486587 + -1.5 Combine like terms: 9.552486587 + -1.5 = 8.052486587 x = 8.052486587 Simplifying x = 8.052486587Subproblem 2
x + 1.5 = -9.552486587 Simplifying x + 1.5 = -9.552486587 Reorder the terms: 1.5 + x = -9.552486587 Solving 1.5 + x = -9.552486587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -9.552486587 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -9.552486587 + -1.5 x = -9.552486587 + -1.5 Combine like terms: -9.552486587 + -1.5 = -11.052486587 x = -11.052486587 Simplifying x = -11.052486587Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.052486587, -11.052486587}
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