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Simplifying 91 = (2x + -3)(x + 1) Reorder the terms: 91 = (-3 + 2x)(x + 1) Reorder the terms: 91 = (-3 + 2x)(1 + x) Multiply (-3 + 2x) * (1 + x) 91 = (-3(1 + x) + 2x * (1 + x)) 91 = ((1 * -3 + x * -3) + 2x * (1 + x)) 91 = ((-3 + -3x) + 2x * (1 + x)) 91 = (-3 + -3x + (1 * 2x + x * 2x)) 91 = (-3 + -3x + (2x + 2x2)) Combine like terms: -3x + 2x = -1x 91 = (-3 + -1x + 2x2) Solving 91 = -3 + -1x + 2x2 Solving for variable 'x'. Combine like terms: 91 + 3 = 94 94 + x + -2x2 = -3 + -1x + 2x2 + 3 + x + -2x2 Reorder the terms: 94 + x + -2x2 = -3 + 3 + -1x + x + 2x2 + -2x2 Combine like terms: -3 + 3 = 0 94 + x + -2x2 = 0 + -1x + x + 2x2 + -2x2 94 + x + -2x2 = -1x + x + 2x2 + -2x2 Combine like terms: -1x + x = 0 94 + x + -2x2 = 0 + 2x2 + -2x2 94 + x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 94 + x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -47 + -0.5x + x2 = 0 Move the constant term to the right: Add '47' to each side of the equation. -47 + -0.5x + 47 + x2 = 0 + 47 Reorder the terms: -47 + 47 + -0.5x + x2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -0.5x + x2 = 0 + 47 -0.5x + x2 = 0 + 47 Combine like terms: 0 + 47 = 47 -0.5x + x2 = 47 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.5x + 0.25 + x2 = 47 + 0.25 Reorder the terms: 0.25 + -0.5x + x2 = 47 + 0.25 Combine like terms: 47 + 0.25 = 47.25 0.25 + -0.5x + x2 = 47.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (x + 0.5) equal to 6.873863542 and -6.873863542.Subproblem 1
x + 0.5 = 6.873863542 Simplifying x + 0.5 = 6.873863542 Reorder the terms: 0.5 + x = 6.873863542 Solving 0.5 + x = 6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.873863542 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.873863542 + -0.5 x = 6.873863542 + -0.5 Combine like terms: 6.873863542 + -0.5 = 6.373863542 x = 6.373863542 Simplifying x = 6.373863542Subproblem 2
x + 0.5 = -6.873863542 Simplifying x + 0.5 = -6.873863542 Reorder the terms: 0.5 + x = -6.873863542 Solving 0.5 + x = -6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.873863542 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.873863542 + -0.5 x = -6.873863542 + -0.5 Combine like terms: -6.873863542 + -0.5 = -7.373863542 x = -7.373863542 Simplifying x = -7.373863542Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.373863542, -7.373863542}
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