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Simplifying 2x(x + -5) = 5x + -1 Reorder the terms: 2x(-5 + x) = 5x + -1 (-5 * 2x + x * 2x) = 5x + -1 (-10x + 2x2) = 5x + -1 Reorder the terms: -10x + 2x2 = -1 + 5x Solving -10x + 2x2 = -1 + 5x Solving for variable 'x'. Reorder the terms: 1 + -10x + -5x + 2x2 = -1 + 5x + 1 + -5x Combine like terms: -10x + -5x = -15x 1 + -15x + 2x2 = -1 + 5x + 1 + -5x Reorder the terms: 1 + -15x + 2x2 = -1 + 1 + 5x + -5x Combine like terms: -1 + 1 = 0 1 + -15x + 2x2 = 0 + 5x + -5x 1 + -15x + 2x2 = 5x + -5x Combine like terms: 5x + -5x = 0 1 + -15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -7.5x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -7.5x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -7.5x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -7.5x + x2 = 0 + -0.5 -7.5x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -7.5x + x2 = -0.5 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = -0.5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = -0.5 + 14.0625 Combine like terms: -0.5 + 14.0625 = 13.5625 14.0625 + -7.5x + x2 = 13.5625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (x + -3.75) equal to 3.682729966 and -3.682729966.Subproblem 1
x + -3.75 = 3.682729966 Simplifying x + -3.75 = 3.682729966 Reorder the terms: -3.75 + x = 3.682729966 Solving -3.75 + x = 3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 3.682729966 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 3.682729966 + 3.75 x = 3.682729966 + 3.75 Combine like terms: 3.682729966 + 3.75 = 7.432729966 x = 7.432729966 Simplifying x = 7.432729966Subproblem 2
x + -3.75 = -3.682729966 Simplifying x + -3.75 = -3.682729966 Reorder the terms: -3.75 + x = -3.682729966 Solving -3.75 + x = -3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -3.682729966 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -3.682729966 + 3.75 x = -3.682729966 + 3.75 Combine like terms: -3.682729966 + 3.75 = 0.067270034 x = 0.067270034 Simplifying x = 0.067270034Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.432729966, 0.067270034}
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