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Simplifying 5(2x2 + 35x + -50) = 0 Reorder the terms: 5(-50 + 35x + 2x2) = 0 (-50 * 5 + 35x * 5 + 2x2 * 5) = 0 (-250 + 175x + 10x2) = 0 Solving -250 + 175x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-50 + 35x + 2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-50 + 35x + 2x2)' equal to zero and attempt to solve: Simplifying -50 + 35x + 2x2 = 0 Solving -50 + 35x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -25 + 17.5x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 17.5x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 17.5x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 17.5x + x2 = 0 + 25 17.5x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 17.5x + x2 = 25 The x term is 17.5x. Take half its coefficient (8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. 17.5x + 76.5625 + x2 = 25 + 76.5625 Reorder the terms: 76.5625 + 17.5x + x2 = 25 + 76.5625 Combine like terms: 25 + 76.5625 = 101.5625 76.5625 + 17.5x + x2 = 101.5625 Factor a perfect square on the left side: (x + 8.75)(x + 8.75) = 101.5625 Calculate the square root of the right side: 10.077822185 Break this problem into two subproblems by setting (x + 8.75) equal to 10.077822185 and -10.077822185.Subproblem 1
x + 8.75 = 10.077822185 Simplifying x + 8.75 = 10.077822185 Reorder the terms: 8.75 + x = 10.077822185 Solving 8.75 + x = 10.077822185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = 10.077822185 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = 10.077822185 + -8.75 x = 10.077822185 + -8.75 Combine like terms: 10.077822185 + -8.75 = 1.327822185 x = 1.327822185 Simplifying x = 1.327822185Subproblem 2
x + 8.75 = -10.077822185 Simplifying x + 8.75 = -10.077822185 Reorder the terms: 8.75 + x = -10.077822185 Solving 8.75 + x = -10.077822185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = -10.077822185 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = -10.077822185 + -8.75 x = -10.077822185 + -8.75 Combine like terms: -10.077822185 + -8.75 = -18.827822185 x = -18.827822185 Simplifying x = -18.827822185Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.327822185, -18.827822185}Solution
x = {1.327822185, -18.827822185}
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