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Simplifying 5(x) = 3 + -5x + -2x2 Solving 5x = 3 + -5x + -2x2 Solving for variable 'x'. Reorder the terms: -3 + 5x + 5x + 2x2 = 3 + -5x + -2x2 + -3 + 5x + 2x2 Combine like terms: 5x + 5x = 10x -3 + 10x + 2x2 = 3 + -5x + -2x2 + -3 + 5x + 2x2 Reorder the terms: -3 + 10x + 2x2 = 3 + -3 + -5x + 5x + -2x2 + 2x2 Combine like terms: 3 + -3 = 0 -3 + 10x + 2x2 = 0 + -5x + 5x + -2x2 + 2x2 -3 + 10x + 2x2 = -5x + 5x + -2x2 + 2x2 Combine like terms: -5x + 5x = 0 -3 + 10x + 2x2 = 0 + -2x2 + 2x2 -3 + 10x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -3 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + 5x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 5x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 5x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 5x + x2 = 0 + 1.5 5x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 5x + x2 = 1.5 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 = 1.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 1.5 + 6.25 Combine like terms: 1.5 + 6.25 = 7.75 6.25 + 5x + x2 = 7.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (x + 2.5) equal to 2.783882181 and -2.783882181.Subproblem 1
x + 2.5 = 2.783882181 Simplifying x + 2.5 = 2.783882181 Reorder the terms: 2.5 + x = 2.783882181 Solving 2.5 + x = 2.783882181 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 = 2.783882181 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.783882181 + -2.5 x = 2.783882181 + -2.5 Combine like terms: 2.783882181 + -2.5 = 0.283882181 x = 0.283882181 Simplifying x = 0.283882181Subproblem 2
x + 2.5 = -2.783882181 Simplifying x + 2.5 = -2.783882181 Reorder the terms: 2.5 + x = -2.783882181 Solving 2.5 + x = -2.783882181 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 = -2.783882181 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.783882181 + -2.5 x = -2.783882181 + -2.5 Combine like terms: -2.783882181 + -2.5 = -5.283882181 x = -5.283882181 Simplifying x = -5.283882181Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.283882181, -5.283882181}
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