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Simplifying 5x(x + -1) = 39 Reorder the terms: 5x(-1 + x) = 39 (-1 * 5x + x * 5x) = 39 (-5x + 5x2) = 39 Solving -5x + 5x2 = 39 Solving for variable 'x'. Reorder the terms: -39 + -5x + 5x2 = 39 + -39 Combine like terms: 39 + -39 = 0 -39 + -5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.8 + -1x + x2 = 0 Move the constant term to the right: Add '7.8' to each side of the equation. -7.8 + -1x + 7.8 + x2 = 0 + 7.8 Reorder the terms: -7.8 + 7.8 + -1x + x2 = 0 + 7.8 Combine like terms: -7.8 + 7.8 = 0.0 0.0 + -1x + x2 = 0 + 7.8 -1x + x2 = 0 + 7.8 Combine like terms: 0 + 7.8 = 7.8 -1x + x2 = 7.8 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 7.8 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 7.8 + 0.25 Combine like terms: 7.8 + 0.25 = 8.05 0.25 + -1x + x2 = 8.05 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 8.05 Calculate the square root of the right side: 2.837252192 Break this problem into two subproblems by setting (x + -0.5) equal to 2.837252192 and -2.837252192.Subproblem 1
x + -0.5 = 2.837252192 Simplifying x + -0.5 = 2.837252192 Reorder the terms: -0.5 + x = 2.837252192 Solving -0.5 + x = 2.837252192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.837252192 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.837252192 + 0.5 x = 2.837252192 + 0.5 Combine like terms: 2.837252192 + 0.5 = 3.337252192 x = 3.337252192 Simplifying x = 3.337252192Subproblem 2
x + -0.5 = -2.837252192 Simplifying x + -0.5 = -2.837252192 Reorder the terms: -0.5 + x = -2.837252192 Solving -0.5 + x = -2.837252192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.837252192 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.837252192 + 0.5 x = -2.837252192 + 0.5 Combine like terms: -2.837252192 + 0.5 = -2.337252192 x = -2.337252192 Simplifying x = -2.337252192Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.337252192, -2.337252192}
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