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Simplifying x(2x + -5) = 85 Reorder the terms: x(-5 + 2x) = 85 (-5 * x + 2x * x) = 85 (-5x + 2x2) = 85 Solving -5x + 2x2 = 85 Solving for variable 'x'. Reorder the terms: -85 + -5x + 2x2 = 85 + -85 Combine like terms: 85 + -85 = 0 -85 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -42.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '42.5' to each side of the equation. -42.5 + -2.5x + 42.5 + x2 = 0 + 42.5 Reorder the terms: -42.5 + 42.5 + -2.5x + x2 = 0 + 42.5 Combine like terms: -42.5 + 42.5 = 0.0 0.0 + -2.5x + x2 = 0 + 42.5 -2.5x + x2 = 0 + 42.5 Combine like terms: 0 + 42.5 = 42.5 -2.5x + x2 = 42.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 42.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 42.5 + 1.5625 Combine like terms: 42.5 + 1.5625 = 44.0625 1.5625 + -2.5x + x2 = 44.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 44.0625 Calculate the square root of the right side: 6.637959024 Break this problem into two subproblems by setting (x + -1.25) equal to 6.637959024 and -6.637959024.Subproblem 1
x + -1.25 = 6.637959024 Simplifying x + -1.25 = 6.637959024 Reorder the terms: -1.25 + x = 6.637959024 Solving -1.25 + x = 6.637959024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 6.637959024 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 6.637959024 + 1.25 x = 6.637959024 + 1.25 Combine like terms: 6.637959024 + 1.25 = 7.887959024 x = 7.887959024 Simplifying x = 7.887959024Subproblem 2
x + -1.25 = -6.637959024 Simplifying x + -1.25 = -6.637959024 Reorder the terms: -1.25 + x = -6.637959024 Solving -1.25 + x = -6.637959024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -6.637959024 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -6.637959024 + 1.25 x = -6.637959024 + 1.25 Combine like terms: -6.637959024 + 1.25 = -5.387959024 x = -5.387959024 Simplifying x = -5.387959024Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.887959024, -5.387959024}
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