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Simplifying 0 = 0.5x2 + 5x + 12.5 Reorder the terms: 0 = 12.5 + 5x + 0.5x2 Solving 0 = 12.5 + 5x + 0.5x2 Solving for variable 'x'. Combine like terms: 0 + -12.5 = -12.5 -12.5 + -5x + -0.5x2 = 12.5 + 5x + 0.5x2 + -12.5 + -5x + -0.5x2 Reorder the terms: -12.5 + -5x + -0.5x2 = 12.5 + -12.5 + 5x + -5x + 0.5x2 + -0.5x2 Combine like terms: 12.5 + -12.5 = 0.0 -12.5 + -5x + -0.5x2 = 0.0 + 5x + -5x + 0.5x2 + -0.5x2 -12.5 + -5x + -0.5x2 = 5x + -5x + 0.5x2 + -0.5x2 Combine like terms: 5x + -5x = 0 -12.5 + -5x + -0.5x2 = 0 + 0.5x2 + -0.5x2 -12.5 + -5x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 -12.5 + -5x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 25 + 10x + x2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + 10x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + 10x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 10x + x2 = 0 + -25 10x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 10x + x2 = -25 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -25 + 25 Reorder the terms: 25 + 10x + x2 = -25 + 25 Combine like terms: -25 + 25 = 0 25 + 10x + x2 = 0 Factor a perfect square on the left side: (x + 5)(x + 5) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x + 5) equal to 0 and 0.Subproblem 1
x + 5 = 0 Simplifying x + 5 = 0 Reorder the terms: 5 + x = 0 Solving 5 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 2
x + 5 = 0 Simplifying x + 5 = 0 Reorder the terms: 5 + x = 0 Solving 5 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5, -5}
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