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Simplifying 500(6 + -1x)(3 + -1x) = 500 Multiply (6 + -1x) * (3 + -1x) 500(6(3 + -1x) + -1x * (3 + -1x)) = 500 500((3 * 6 + -1x * 6) + -1x * (3 + -1x)) = 500 500((18 + -6x) + -1x * (3 + -1x)) = 500 500(18 + -6x + (3 * -1x + -1x * -1x)) = 500 500(18 + -6x + (-3x + 1x2)) = 500 Combine like terms: -6x + -3x = -9x 500(18 + -9x + 1x2) = 500 (18 * 500 + -9x * 500 + 1x2 * 500) = 500 (9000 + -4500x + 500x2) = 500 Solving 9000 + -4500x + 500x2 = 500 Solving for variable 'x'. Reorder the terms: 9000 + -500 + -4500x + 500x2 = 500 + -500 Combine like terms: 9000 + -500 = 8500 8500 + -4500x + 500x2 = 500 + -500 Combine like terms: 500 + -500 = 0 8500 + -4500x + 500x2 = 0 Factor out the Greatest Common Factor (GCF), '500'. 500(17 + -9x + x2) = 0 Ignore the factor 500.Subproblem 1
Set the factor '(17 + -9x + x2)' equal to zero and attempt to solve: Simplifying 17 + -9x + x2 = 0 Solving 17 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -9x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + -9x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -9x + x2 = 0 + -17 -9x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 -9x + x2 = -17 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -17 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -17 + 20.25 Combine like terms: -17 + 20.25 = 3.25 20.25 + -9x + x2 = 3.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + -4.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + -4.5 = 1.802775638 Simplifying x + -4.5 = 1.802775638 Reorder the terms: -4.5 + x = 1.802775638 Solving -4.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 1.802775638 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 1.802775638 + 4.5 x = 1.802775638 + 4.5 Combine like terms: 1.802775638 + 4.5 = 6.302775638 x = 6.302775638 Simplifying x = 6.302775638Subproblem 2
x + -4.5 = -1.802775638 Simplifying x + -4.5 = -1.802775638 Reorder the terms: -4.5 + x = -1.802775638 Solving -4.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -1.802775638 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -1.802775638 + 4.5 x = -1.802775638 + 4.5 Combine like terms: -1.802775638 + 4.5 = 2.697224362 x = 2.697224362 Simplifying x = 2.697224362Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.302775638, 2.697224362}Solution
x = {6.302775638, 2.697224362}
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