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Simplifying 35 = (2x + 5)(2x + 7) + -96 Reorder the terms: 35 = (5 + 2x)(2x + 7) + -96 Reorder the terms: 35 = (5 + 2x)(7 + 2x) + -96 Multiply (5 + 2x) * (7 + 2x) 35 = (5(7 + 2x) + 2x * (7 + 2x)) + -96 35 = ((7 * 5 + 2x * 5) + 2x * (7 + 2x)) + -96 35 = ((35 + 10x) + 2x * (7 + 2x)) + -96 35 = (35 + 10x + (7 * 2x + 2x * 2x)) + -96 35 = (35 + 10x + (14x + 4x2)) + -96 Combine like terms: 10x + 14x = 24x 35 = (35 + 24x + 4x2) + -96 Reorder the terms: 35 = 35 + -96 + 24x + 4x2 Combine like terms: 35 + -96 = -61 35 = -61 + 24x + 4x2 Solving 35 = -61 + 24x + 4x2 Solving for variable 'x'. Combine like terms: 35 + 61 = 96 96 + -24x + -4x2 = -61 + 24x + 4x2 + 61 + -24x + -4x2 Reorder the terms: 96 + -24x + -4x2 = -61 + 61 + 24x + -24x + 4x2 + -4x2 Combine like terms: -61 + 61 = 0 96 + -24x + -4x2 = 0 + 24x + -24x + 4x2 + -4x2 96 + -24x + -4x2 = 24x + -24x + 4x2 + -4x2 Combine like terms: 24x + -24x = 0 96 + -24x + -4x2 = 0 + 4x2 + -4x2 96 + -24x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 96 + -24x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(24 + -6x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(24 + -6x + -1x2)' equal to zero and attempt to solve: Simplifying 24 + -6x + -1x2 = 0 Solving 24 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24 + 6x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 6x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 6x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 6x + x2 = 0 + 24 6x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 6x + x2 = 24 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 24 + 9 Reorder the terms: 9 + 6x + x2 = 24 + 9 Combine like terms: 24 + 9 = 33 9 + 6x + x2 = 33 Factor a perfect square on the left side: (x + 3)(x + 3) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + 3) equal to 5.744562647 and -5.744562647.Subproblem 1
x + 3 = 5.744562647 Simplifying x + 3 = 5.744562647 Reorder the terms: 3 + x = 5.744562647 Solving 3 + x = 5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5.744562647 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.744562647 + -3 x = 5.744562647 + -3 Combine like terms: 5.744562647 + -3 = 2.744562647 x = 2.744562647 Simplifying x = 2.744562647Subproblem 2
x + 3 = -5.744562647 Simplifying x + 3 = -5.744562647 Reorder the terms: 3 + x = -5.744562647 Solving 3 + x = -5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5.744562647 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.744562647 + -3 x = -5.744562647 + -3 Combine like terms: -5.744562647 + -3 = -8.744562647 x = -8.744562647 Simplifying x = -8.744562647Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.744562647, -8.744562647}Solution
x = {2.744562647, -8.744562647}
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