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Simplifying 0.5x2 + 2.5x + -1.5 = 0 Reorder the terms: -1.5 + 2.5x + 0.5x2 = 0 Solving -1.5 + 2.5x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -3 + 5x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 5x + x2 = 0 + 3 5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 5x + x2 = 3 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 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 3 + 6.25 Combine like terms: 3 + 6.25 = 9.25 6.25 + 5x + x2 = 9.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x + 2.5) equal to 3.041381265 and -3.041381265.Subproblem 1
x + 2.5 = 3.041381265 Simplifying x + 2.5 = 3.041381265 Reorder the terms: 2.5 + x = 3.041381265 Solving 2.5 + x = 3.041381265 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 = 3.041381265 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.041381265 + -2.5 x = 3.041381265 + -2.5 Combine like terms: 3.041381265 + -2.5 = 0.541381265 x = 0.541381265 Simplifying x = 0.541381265Subproblem 2
x + 2.5 = -3.041381265 Simplifying x + 2.5 = -3.041381265 Reorder the terms: 2.5 + x = -3.041381265 Solving 2.5 + x = -3.041381265 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 = -3.041381265 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.041381265 + -2.5 x = -3.041381265 + -2.5 Combine like terms: -3.041381265 + -2.5 = -5.541381265 x = -5.541381265 Simplifying x = -5.541381265Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.541381265, -5.541381265}
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