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Simplifying 75x = (2x + -5)(2x + 5) Reorder the terms: 75x = (-5 + 2x)(2x + 5) Reorder the terms: 75x = (-5 + 2x)(5 + 2x) Multiply (-5 + 2x) * (5 + 2x) 75x = (-5(5 + 2x) + 2x * (5 + 2x)) 75x = ((5 * -5 + 2x * -5) + 2x * (5 + 2x)) 75x = ((-25 + -10x) + 2x * (5 + 2x)) 75x = (-25 + -10x + (5 * 2x + 2x * 2x)) 75x = (-25 + -10x + (10x + 4x2)) Combine like terms: -10x + 10x = 0 75x = (-25 + 0 + 4x2) 75x = (-25 + 4x2) Solving 75x = -25 + 4x2 Solving for variable 'x'. Reorder the terms: 25 + 75x + -4x2 = -25 + 4x2 + 25 + -4x2 Reorder the terms: 25 + 75x + -4x2 = -25 + 25 + 4x2 + -4x2 Combine like terms: -25 + 25 = 0 25 + 75x + -4x2 = 0 + 4x2 + -4x2 25 + 75x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 25 + 75x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -6.25 + -18.75x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -18.75x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -18.75x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -18.75x + x2 = 0 + 6.25 -18.75x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -18.75x + x2 = 6.25 The x term is -18.75x. Take half its coefficient (-9.375). Square it (87.890625) and add it to both sides. Add '87.890625' to each side of the equation. -18.75x + 87.890625 + x2 = 6.25 + 87.890625 Reorder the terms: 87.890625 + -18.75x + x2 = 6.25 + 87.890625 Combine like terms: 6.25 + 87.890625 = 94.140625 87.890625 + -18.75x + x2 = 94.140625 Factor a perfect square on the left side: (x + -9.375)(x + -9.375) = 94.140625 Calculate the square root of the right side: 9.702609185 Break this problem into two subproblems by setting (x + -9.375) equal to 9.702609185 and -9.702609185.Subproblem 1
x + -9.375 = 9.702609185 Simplifying x + -9.375 = 9.702609185 Reorder the terms: -9.375 + x = 9.702609185 Solving -9.375 + x = 9.702609185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.375' to each side of the equation. -9.375 + 9.375 + x = 9.702609185 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + x = 9.702609185 + 9.375 x = 9.702609185 + 9.375 Combine like terms: 9.702609185 + 9.375 = 19.077609185 x = 19.077609185 Simplifying x = 19.077609185Subproblem 2
x + -9.375 = -9.702609185 Simplifying x + -9.375 = -9.702609185 Reorder the terms: -9.375 + x = -9.702609185 Solving -9.375 + x = -9.702609185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.375' to each side of the equation. -9.375 + 9.375 + x = -9.702609185 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + x = -9.702609185 + 9.375 x = -9.702609185 + 9.375 Combine like terms: -9.702609185 + 9.375 = -0.327609185 x = -0.327609185 Simplifying x = -0.327609185Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.077609185, -0.327609185}
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