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Simplifying 5x(x + -1) + -3x(x + -2) = 2 Reorder the terms: 5x(-1 + x) + -3x(x + -2) = 2 (-1 * 5x + x * 5x) + -3x(x + -2) = 2 (-5x + 5x2) + -3x(x + -2) = 2 Reorder the terms: -5x + 5x2 + -3x(-2 + x) = 2 -5x + 5x2 + (-2 * -3x + x * -3x) = 2 -5x + 5x2 + (6x + -3x2) = 2 Reorder the terms: -5x + 6x + 5x2 + -3x2 = 2 Combine like terms: -5x + 6x = 1x 1x + 5x2 + -3x2 = 2 Combine like terms: 5x2 + -3x2 = 2x2 1x + 2x2 = 2 Solving 1x + 2x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 1x + 2x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1 + 0.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.5x + x2 = 0 + 1 0.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.5x + x2 = 1 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 1 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 1 + 0.0625 Combine like terms: 1 + 0.0625 = 1.0625 0.0625 + 0.5x + x2 = 1.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x + 0.25) equal to 1.030776406 and -1.030776406.Subproblem 1
x + 0.25 = 1.030776406 Simplifying x + 0.25 = 1.030776406 Reorder the terms: 0.25 + x = 1.030776406 Solving 0.25 + x = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.030776406 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.030776406 + -0.25 x = 1.030776406 + -0.25 Combine like terms: 1.030776406 + -0.25 = 0.780776406 x = 0.780776406 Simplifying x = 0.780776406Subproblem 2
x + 0.25 = -1.030776406 Simplifying x + 0.25 = -1.030776406 Reorder the terms: 0.25 + x = -1.030776406 Solving 0.25 + x = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.030776406 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.030776406 + -0.25 x = -1.030776406 + -0.25 Combine like terms: -1.030776406 + -0.25 = -1.280776406 x = -1.280776406 Simplifying x = -1.280776406Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.780776406, -1.280776406}
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