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Simplifying (2x + -5)(3x) = 125 Reorder the terms: (-5 + 2x)(3x) = 125 Remove parenthesis around (3x) (-5 + 2x) * 3x = 125 Reorder the terms for easier multiplication: 3x(-5 + 2x) = 125 (-5 * 3x + 2x * 3x) = 125 (-15x + 6x2) = 125 Solving -15x + 6x2 = 125 Solving for variable 'x'. Reorder the terms: -125 + -15x + 6x2 = 125 + -125 Combine like terms: 125 + -125 = 0 -125 + -15x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -20.83333333 + -2.5x + x2 = 0 Move the constant term to the right: Add '20.83333333' to each side of the equation. -20.83333333 + -2.5x + 20.83333333 + x2 = 0 + 20.83333333 Reorder the terms: -20.83333333 + 20.83333333 + -2.5x + x2 = 0 + 20.83333333 Combine like terms: -20.83333333 + 20.83333333 = 0.00000000 0.00000000 + -2.5x + x2 = 0 + 20.83333333 -2.5x + x2 = 0 + 20.83333333 Combine like terms: 0 + 20.83333333 = 20.83333333 -2.5x + x2 = 20.83333333 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 = 20.83333333 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 20.83333333 + 1.5625 Combine like terms: 20.83333333 + 1.5625 = 22.39583333 1.5625 + -2.5x + x2 = 22.39583333 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 22.39583333 Calculate the square root of the right side: 4.732423621 Break this problem into two subproblems by setting (x + -1.25) equal to 4.732423621 and -4.732423621.Subproblem 1
x + -1.25 = 4.732423621 Simplifying x + -1.25 = 4.732423621 Reorder the terms: -1.25 + x = 4.732423621 Solving -1.25 + x = 4.732423621 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 = 4.732423621 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 4.732423621 + 1.25 x = 4.732423621 + 1.25 Combine like terms: 4.732423621 + 1.25 = 5.982423621 x = 5.982423621 Simplifying x = 5.982423621Subproblem 2
x + -1.25 = -4.732423621 Simplifying x + -1.25 = -4.732423621 Reorder the terms: -1.25 + x = -4.732423621 Solving -1.25 + x = -4.732423621 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 = -4.732423621 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -4.732423621 + 1.25 x = -4.732423621 + 1.25 Combine like terms: -4.732423621 + 1.25 = -3.482423621 x = -3.482423621 Simplifying x = -3.482423621Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.982423621, -3.482423621}
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