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Simplifying 0 = -25x2 + 500x + -350 Reorder the terms: 0 = -350 + 500x + -25x2 Solving 0 = -350 + 500x + -25x2 Solving for variable 'x'. Combine like terms: 0 + 350 = 350 350 + -500x + 25x2 = -350 + 500x + -25x2 + 350 + -500x + 25x2 Reorder the terms: 350 + -500x + 25x2 = -350 + 350 + 500x + -500x + -25x2 + 25x2 Combine like terms: -350 + 350 = 0 350 + -500x + 25x2 = 0 + 500x + -500x + -25x2 + 25x2 350 + -500x + 25x2 = 500x + -500x + -25x2 + 25x2 Combine like terms: 500x + -500x = 0 350 + -500x + 25x2 = 0 + -25x2 + 25x2 350 + -500x + 25x2 = -25x2 + 25x2 Combine like terms: -25x2 + 25x2 = 0 350 + -500x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '25'. 25(14 + -20x + x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(14 + -20x + x2)' equal to zero and attempt to solve: Simplifying 14 + -20x + x2 = 0 Solving 14 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -20x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -20x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -20x + x2 = 0 + -14 -20x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -20x + x2 = -14 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -14 + 100 Reorder the terms: 100 + -20x + x2 = -14 + 100 Combine like terms: -14 + 100 = 86 100 + -20x + x2 = 86 Factor a perfect square on the left side: (x + -10)(x + -10) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (x + -10) equal to 9.273618495 and -9.273618495.Subproblem 1
x + -10 = 9.273618495 Simplifying x + -10 = 9.273618495 Reorder the terms: -10 + x = 9.273618495 Solving -10 + x = 9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 9.273618495 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.273618495 + 10 x = 9.273618495 + 10 Combine like terms: 9.273618495 + 10 = 19.273618495 x = 19.273618495 Simplifying x = 19.273618495Subproblem 2
x + -10 = -9.273618495 Simplifying x + -10 = -9.273618495 Reorder the terms: -10 + x = -9.273618495 Solving -10 + x = -9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -9.273618495 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.273618495 + 10 x = -9.273618495 + 10 Combine like terms: -9.273618495 + 10 = 0.726381505 x = 0.726381505 Simplifying x = 0.726381505Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.273618495, 0.726381505}Solution
x = {19.273618495, 0.726381505}
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