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Simplifying (2x + -3)(x) = 50 Reorder the terms: (-3 + 2x)(x) = 50 Reorder the terms for easier multiplication: x(-3 + 2x) = 50 (-3 * x + 2x * x) = 50 (-3x + 2x2) = 50 Solving -3x + 2x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + -3x + 2x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -25 + -1.5x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -1.5x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -1.5x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -1.5x + x2 = 0 + 25 -1.5x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -1.5x + x2 = 25 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 25 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 25 + 0.5625 Combine like terms: 25 + 0.5625 = 25.5625 0.5625 + -1.5x + x2 = 25.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 25.5625 Calculate the square root of the right side: 5.055937104 Break this problem into two subproblems by setting (x + -0.75) equal to 5.055937104 and -5.055937104.Subproblem 1
x + -0.75 = 5.055937104 Simplifying x + -0.75 = 5.055937104 Reorder the terms: -0.75 + x = 5.055937104 Solving -0.75 + x = 5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 5.055937104 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 5.055937104 + 0.75 x = 5.055937104 + 0.75 Combine like terms: 5.055937104 + 0.75 = 5.805937104 x = 5.805937104 Simplifying x = 5.805937104Subproblem 2
x + -0.75 = -5.055937104 Simplifying x + -0.75 = -5.055937104 Reorder the terms: -0.75 + x = -5.055937104 Solving -0.75 + x = -5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -5.055937104 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -5.055937104 + 0.75 x = -5.055937104 + 0.75 Combine like terms: -5.055937104 + 0.75 = -4.305937104 x = -4.305937104 Simplifying x = -4.305937104Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.805937104, -4.305937104}
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