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Simplifying 0 = x2 + 5x + 6.25 Reorder the terms: 0 = 6.25 + 5x + x2 Solving 0 = 6.25 + 5x + x2 Solving for variable 'x'. Combine like terms: 0 + -6.25 = -6.25 -6.25 + -5x + -1x2 = 6.25 + 5x + x2 + -6.25 + -5x + -1x2 Reorder the terms: -6.25 + -5x + -1x2 = 6.25 + -6.25 + 5x + -5x + x2 + -1x2 Combine like terms: 6.25 + -6.25 = 0.00 -6.25 + -5x + -1x2 = 0.00 + 5x + -5x + x2 + -1x2 -6.25 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 -6.25 + -5x + -1x2 = 0 + x2 + -1x2 -6.25 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -6.25 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6.25 + 5x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + 5x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + 5x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + 5x + x2 = 0 + -6.25 5x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 5x + x2 = -6.25 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 = -6.25 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -6.25 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 6.25 + 5x + x2 = 0.00 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + 2.5) equal to 0.00 and 0.00.Subproblem 1
x + 2.5 = 0.00 Simplifying x + 2.5 = 0.00 Reorder the terms: 2.5 + x = 0.00 Solving 2.5 + x = 0.00 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 = 0.00 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 0.00 + -2.5 x = 0.00 + -2.5 Combine like terms: 0.00 + -2.5 = -2.5 x = -2.5 Simplifying x = -2.5Subproblem 2
x + 2.5 = 0.00 Simplifying x + 2.5 = 0.00 Reorder the terms: 2.5 + x = 0.00 Solving 2.5 + x = 0.00 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 = 0.00 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 0.00 + -2.5 x = 0.00 + -2.5 Combine like terms: 0.00 + -2.5 = -2.5 x = -2.5 Simplifying x = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.5, -2.5}
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