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Simplifying 88 = (8 + 2x)(11 + 2x) + -88 Multiply (8 + 2x) * (11 + 2x) 88 = (8(11 + 2x) + 2x * (11 + 2x)) + -88 88 = ((11 * 8 + 2x * 8) + 2x * (11 + 2x)) + -88 88 = ((88 + 16x) + 2x * (11 + 2x)) + -88 88 = (88 + 16x + (11 * 2x + 2x * 2x)) + -88 88 = (88 + 16x + (22x + 4x2)) + -88 Combine like terms: 16x + 22x = 38x 88 = (88 + 38x + 4x2) + -88 Reorder the terms: 88 = 88 + -88 + 38x + 4x2 Combine like terms: 88 + -88 = 0 88 = 0 + 38x + 4x2 88 = 38x + 4x2 Solving 88 = 38x + 4x2 Solving for variable 'x'. Reorder the terms: 88 + -38x + -4x2 = 38x + -38x + 4x2 + -4x2 Combine like terms: 38x + -38x = 0 88 + -38x + -4x2 = 0 + 4x2 + -4x2 88 + -38x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 88 + -38x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(44 + -19x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(44 + -19x + -2x2)' equal to zero and attempt to solve: Simplifying 44 + -19x + -2x2 = 0 Solving 44 + -19x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -22 + 9.5x + x2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + 9.5x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 9.5x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 9.5x + x2 = 0 + 22 9.5x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 9.5x + x2 = 22 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = 22 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 22 + 22.5625 Combine like terms: 22 + 22.5625 = 44.5625 22.5625 + 9.5x + x2 = 44.5625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 44.5625 Calculate the square root of the right side: 6.675514961 Break this problem into two subproblems by setting (x + 4.75) equal to 6.675514961 and -6.675514961.Subproblem 1
x + 4.75 = 6.675514961 Simplifying x + 4.75 = 6.675514961 Reorder the terms: 4.75 + x = 6.675514961 Solving 4.75 + x = 6.675514961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 6.675514961 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 6.675514961 + -4.75 x = 6.675514961 + -4.75 Combine like terms: 6.675514961 + -4.75 = 1.925514961 x = 1.925514961 Simplifying x = 1.925514961Subproblem 2
x + 4.75 = -6.675514961 Simplifying x + 4.75 = -6.675514961 Reorder the terms: 4.75 + x = -6.675514961 Solving 4.75 + x = -6.675514961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -6.675514961 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -6.675514961 + -4.75 x = -6.675514961 + -4.75 Combine like terms: -6.675514961 + -4.75 = -11.425514961 x = -11.425514961 Simplifying x = -11.425514961Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.925514961, -11.425514961}Solution
x = {1.925514961, -11.425514961}
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