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Simplifying -2(x + 5) * 5x = -31 Reorder the terms: -2(5 + x) * 5x = -31 Reorder the terms for easier multiplication: -2 * 5x(5 + x) = -31 Multiply -2 * 5 -10x(5 + x) = -31 (5 * -10x + x * -10x) = -31 (-50x + -10x2) = -31 Solving -50x + -10x2 = -31 Solving for variable 'x'. Reorder the terms: 31 + -50x + -10x2 = -31 + 31 Combine like terms: -31 + 31 = 0 31 + -50x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -3.1 + 5x + x2 = 0.0 Move the constant term to the right: Add '3.1' to each side of the equation. -3.1 + 5x + 3.1 + x2 = 0.0 + 3.1 Reorder the terms: -3.1 + 3.1 + 5x + x2 = 0.0 + 3.1 Combine like terms: -3.1 + 3.1 = 0.0 0.0 + 5x + x2 = 0.0 + 3.1 5x + x2 = 0.0 + 3.1 Combine like terms: 0.0 + 3.1 = 3.1 5x + x2 = 3.1 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 3.1 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 3.1 + 6.25 Combine like terms: 3.1 + 6.25 = 9.35 6.25 + 5x + x2 = 9.35 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 9.35 Calculate the square root of the right side: 3.05777697 Break this problem into two subproblems by setting (x + 2.5) equal to 3.05777697 and -3.05777697.Subproblem 1
x + 2.5 = 3.05777697 Simplifying x + 2.5 = 3.05777697 Reorder the terms: 2.5 + x = 3.05777697 Solving 2.5 + x = 3.05777697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.05777697 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.05777697 + -2.5 x = 3.05777697 + -2.5 Combine like terms: 3.05777697 + -2.5 = 0.55777697 x = 0.55777697 Simplifying x = 0.55777697Subproblem 2
x + 2.5 = -3.05777697 Simplifying x + 2.5 = -3.05777697 Reorder the terms: 2.5 + x = -3.05777697 Solving 2.5 + x = -3.05777697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.05777697 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.05777697 + -2.5 x = -3.05777697 + -2.5 Combine like terms: -3.05777697 + -2.5 = -5.55777697 x = -5.55777697 Simplifying x = -5.55777697Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.55777697, -5.55777697}
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