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Simplifying (x + -5)(x + 2) = 53 Reorder the terms: (-5 + x)(x + 2) = 53 Reorder the terms: (-5 + x)(2 + x) = 53 Multiply (-5 + x) * (2 + x) (-5(2 + x) + x(2 + x)) = 53 ((2 * -5 + x * -5) + x(2 + x)) = 53 ((-10 + -5x) + x(2 + x)) = 53 (-10 + -5x + (2 * x + x * x)) = 53 (-10 + -5x + (2x + x2)) = 53 Combine like terms: -5x + 2x = -3x (-10 + -3x + x2) = 53 Solving -10 + -3x + x2 = 53 Solving for variable 'x'. Reorder the terms: -10 + -53 + -3x + x2 = 53 + -53 Combine like terms: -10 + -53 = -63 -63 + -3x + x2 = 53 + -53 Combine like terms: 53 + -53 = 0 -63 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + -3x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + -3x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + -3x + x2 = 0 + 63 -3x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 -3x + x2 = 63 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 = 63 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 63 + 2.25 Combine like terms: 63 + 2.25 = 65.25 2.25 + -3x + x2 = 65.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 65.25 Calculate the square root of the right side: 8.077747211 Break this problem into two subproblems by setting (x + -1.5) equal to 8.077747211 and -8.077747211.Subproblem 1
x + -1.5 = 8.077747211 Simplifying x + -1.5 = 8.077747211 Reorder the terms: -1.5 + x = 8.077747211 Solving -1.5 + x = 8.077747211 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 = 8.077747211 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 8.077747211 + 1.5 x = 8.077747211 + 1.5 Combine like terms: 8.077747211 + 1.5 = 9.577747211 x = 9.577747211 Simplifying x = 9.577747211Subproblem 2
x + -1.5 = -8.077747211 Simplifying x + -1.5 = -8.077747211 Reorder the terms: -1.5 + x = -8.077747211 Solving -1.5 + x = -8.077747211 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 = -8.077747211 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -8.077747211 + 1.5 x = -8.077747211 + 1.5 Combine like terms: -8.077747211 + 1.5 = -6.577747211 x = -6.577747211 Simplifying x = -6.577747211Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.577747211, -6.577747211}
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