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Simplifying 0 = -1.25x2 + -6.25x + 7.5 Reorder the terms: 0 = 7.5 + -6.25x + -1.25x2 Solving 0 = 7.5 + -6.25x + -1.25x2 Solving for variable 'x'. Combine like terms: 0 + -7.5 = -7.5 -7.5 + 6.25x + 1.25x2 = 7.5 + -6.25x + -1.25x2 + -7.5 + 6.25x + 1.25x2 Reorder the terms: -7.5 + 6.25x + 1.25x2 = 7.5 + -7.5 + -6.25x + 6.25x + -1.25x2 + 1.25x2 Combine like terms: 7.5 + -7.5 = 0.0 -7.5 + 6.25x + 1.25x2 = 0.0 + -6.25x + 6.25x + -1.25x2 + 1.25x2 -7.5 + 6.25x + 1.25x2 = -6.25x + 6.25x + -1.25x2 + 1.25x2 Combine like terms: -6.25x + 6.25x = 0.00 -7.5 + 6.25x + 1.25x2 = 0.00 + -1.25x2 + 1.25x2 -7.5 + 6.25x + 1.25x2 = -1.25x2 + 1.25x2 Combine like terms: -1.25x2 + 1.25x2 = 0.00 -7.5 + 6.25x + 1.25x2 = 0.00 Begin completing the square. Divide all terms by 1.25 the coefficient of the squared term: Divide each side by '1.25'. -6 + 5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 5x + x2 = 0 + 6 5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 5x + x2 = 6 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 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 6 + 6.25 Combine like terms: 6 + 6.25 = 12.25 6.25 + 5x + x2 = 12.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 12.25 Calculate the square root of the right side: 3.5 Break this problem into two subproblems by setting (x + 2.5) equal to 3.5 and -3.5.Subproblem 1
x + 2.5 = 3.5 Simplifying x + 2.5 = 3.5 Reorder the terms: 2.5 + x = 3.5 Solving 2.5 + x = 3.5 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 = 3.5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.5 + -2.5 x = 3.5 + -2.5 Combine like terms: 3.5 + -2.5 = 1 x = 1 Simplifying x = 1Subproblem 2
x + 2.5 = -3.5 Simplifying x + 2.5 = -3.5 Reorder the terms: 2.5 + x = -3.5 Solving 2.5 + x = -3.5 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 = -3.5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.5 + -2.5 x = -3.5 + -2.5 Combine like terms: -3.5 + -2.5 = -6 x = -6 Simplifying x = -6Solution
The solution to the problem is based on the solutions from the subproblems. x = {1, -6}
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