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Simplifying (2x + -5)(5x + -10) = 90 Reorder the terms: (-5 + 2x)(5x + -10) = 90 Reorder the terms: (-5 + 2x)(-10 + 5x) = 90 Multiply (-5 + 2x) * (-10 + 5x) (-5(-10 + 5x) + 2x * (-10 + 5x)) = 90 ((-10 * -5 + 5x * -5) + 2x * (-10 + 5x)) = 90 ((50 + -25x) + 2x * (-10 + 5x)) = 90 (50 + -25x + (-10 * 2x + 5x * 2x)) = 90 (50 + -25x + (-20x + 10x2)) = 90 Combine like terms: -25x + -20x = -45x (50 + -45x + 10x2) = 90 Solving 50 + -45x + 10x2 = 90 Solving for variable 'x'. Reorder the terms: 50 + -90 + -45x + 10x2 = 90 + -90 Combine like terms: 50 + -90 = -40 -40 + -45x + 10x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -40 + -45x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-8 + -9x + 2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-8 + -9x + 2x2)' equal to zero and attempt to solve: Simplifying -8 + -9x + 2x2 = 0 Solving -8 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + -4.5x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -4.5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -4.5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -4.5x + x2 = 0 + 4 -4.5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -4.5x + x2 = 4 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 4 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 4 + 5.0625 Combine like terms: 4 + 5.0625 = 9.0625 5.0625 + -4.5x + x2 = 9.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + -2.25) equal to 3.010398645 and -3.010398645.Subproblem 1
x + -2.25 = 3.010398645 Simplifying x + -2.25 = 3.010398645 Reorder the terms: -2.25 + x = 3.010398645 Solving -2.25 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 3.010398645 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 3.010398645 + 2.25 x = 3.010398645 + 2.25 Combine like terms: 3.010398645 + 2.25 = 5.260398645 x = 5.260398645 Simplifying x = 5.260398645Subproblem 2
x + -2.25 = -3.010398645 Simplifying x + -2.25 = -3.010398645 Reorder the terms: -2.25 + x = -3.010398645 Solving -2.25 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -3.010398645 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -3.010398645 + 2.25 x = -3.010398645 + 2.25 Combine like terms: -3.010398645 + 2.25 = -0.760398645 x = -0.760398645 Simplifying x = -0.760398645Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.260398645, -0.760398645}Solution
x = {5.260398645, -0.760398645}
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