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Simplifying (4x + -5)(4x + 6) = 182 Reorder the terms: (-5 + 4x)(4x + 6) = 182 Reorder the terms: (-5 + 4x)(6 + 4x) = 182 Multiply (-5 + 4x) * (6 + 4x) (-5(6 + 4x) + 4x * (6 + 4x)) = 182 ((6 * -5 + 4x * -5) + 4x * (6 + 4x)) = 182 ((-30 + -20x) + 4x * (6 + 4x)) = 182 (-30 + -20x + (6 * 4x + 4x * 4x)) = 182 (-30 + -20x + (24x + 16x2)) = 182 Combine like terms: -20x + 24x = 4x (-30 + 4x + 16x2) = 182 Solving -30 + 4x + 16x2 = 182 Solving for variable 'x'. Reorder the terms: -30 + -182 + 4x + 16x2 = 182 + -182 Combine like terms: -30 + -182 = -212 -212 + 4x + 16x2 = 182 + -182 Combine like terms: 182 + -182 = 0 -212 + 4x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-53 + x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-53 + x + 4x2)' equal to zero and attempt to solve: Simplifying -53 + x + 4x2 = 0 Solving -53 + x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -13.25 + 0.25x + x2 = 0 Move the constant term to the right: Add '13.25' to each side of the equation. -13.25 + 0.25x + 13.25 + x2 = 0 + 13.25 Reorder the terms: -13.25 + 13.25 + 0.25x + x2 = 0 + 13.25 Combine like terms: -13.25 + 13.25 = 0.00 0.00 + 0.25x + x2 = 0 + 13.25 0.25x + x2 = 0 + 13.25 Combine like terms: 0 + 13.25 = 13.25 0.25x + x2 = 13.25 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. 0.25x + 0.25 + x2 = 13.25 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = 13.25 + 0.25 Combine like terms: 13.25 + 0.25 = 13.5 0.25 + 0.25x + x2 = 13.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 13.5 Calculate the square root of the right side: 3.674234614 Break this problem into two subproblems by setting (x + 0.5) equal to 3.674234614 and -3.674234614.Subproblem 1
x + 0.5 = 3.674234614 Simplifying x + 0.5 = 3.674234614 Reorder the terms: 0.5 + x = 3.674234614 Solving 0.5 + x = 3.674234614 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 = 3.674234614 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.674234614 + -0.5 x = 3.674234614 + -0.5 Combine like terms: 3.674234614 + -0.5 = 3.174234614 x = 3.174234614 Simplifying x = 3.174234614Subproblem 2
x + 0.5 = -3.674234614 Simplifying x + 0.5 = -3.674234614 Reorder the terms: 0.5 + x = -3.674234614 Solving 0.5 + x = -3.674234614 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 = -3.674234614 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.674234614 + -0.5 x = -3.674234614 + -0.5 Combine like terms: -3.674234614 + -0.5 = -4.174234614 x = -4.174234614 Simplifying x = -4.174234614Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.174234614, -4.174234614}Solution
x = {3.174234614, -4.174234614}
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