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Simplifying 0 = x2 + -2.5x + -75 Reorder the terms: 0 = -75 + -2.5x + x2 Solving 0 = -75 + -2.5x + x2 Solving for variable 'x'. Combine like terms: 0 + 75 = 75 75 + 2.5x + -1x2 = -75 + -2.5x + x2 + 75 + 2.5x + -1x2 Reorder the terms: 75 + 2.5x + -1x2 = -75 + 75 + -2.5x + 2.5x + x2 + -1x2 Combine like terms: -75 + 75 = 0 75 + 2.5x + -1x2 = 0 + -2.5x + 2.5x + x2 + -1x2 75 + 2.5x + -1x2 = -2.5x + 2.5x + x2 + -1x2 Combine like terms: -2.5x + 2.5x = 0.0 75 + 2.5x + -1x2 = 0.0 + x2 + -1x2 75 + 2.5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 75 + 2.5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -75 + -2.5x + x2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + -2.5x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + -2.5x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + -2.5x + x2 = 0 + 75 -2.5x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 -2.5x + x2 = 75 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 75 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 75 + 1.5625 Combine like terms: 75 + 1.5625 = 76.5625 1.5625 + -2.5x + x2 = 76.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 76.5625 Calculate the square root of the right side: 8.75 Break this problem into two subproblems by setting (x + -1.25) equal to 8.75 and -8.75.Subproblem 1
x + -1.25 = 8.75 Simplifying x + -1.25 = 8.75 Reorder the terms: -1.25 + x = 8.75 Solving -1.25 + x = 8.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 8.75 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 8.75 + 1.25 x = 8.75 + 1.25 Combine like terms: 8.75 + 1.25 = 10 x = 10 Simplifying x = 10Subproblem 2
x + -1.25 = -8.75 Simplifying x + -1.25 = -8.75 Reorder the terms: -1.25 + x = -8.75 Solving -1.25 + x = -8.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -8.75 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -8.75 + 1.25 x = -8.75 + 1.25 Combine like terms: -8.75 + 1.25 = -7.5 x = -7.5 Simplifying x = -7.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {10, -7.5}
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