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Simplifying -0.5x2 + -2.5x + 18 = 0 Reorder the terms: 18 + -2.5x + -0.5x2 = 0 Solving 18 + -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'. -36 + 5x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + 5x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 5x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 5x + x2 = 0 + 36 5x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 5x + x2 = 36 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 = 36 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 36 + 6.25 Combine like terms: 36 + 6.25 = 42.25 6.25 + 5x + x2 = 42.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 42.25 Calculate the square root of the right side: 6.5 Break this problem into two subproblems by setting (x + 2.5) equal to 6.5 and -6.5.Subproblem 1
x + 2.5 = 6.5 Simplifying x + 2.5 = 6.5 Reorder the terms: 2.5 + x = 6.5 Solving 2.5 + x = 6.5 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 = 6.5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 6.5 + -2.5 x = 6.5 + -2.5 Combine like terms: 6.5 + -2.5 = 4 x = 4 Simplifying x = 4Subproblem 2
x + 2.5 = -6.5 Simplifying x + 2.5 = -6.5 Reorder the terms: 2.5 + x = -6.5 Solving 2.5 + x = -6.5 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 = -6.5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -6.5 + -2.5 x = -6.5 + -2.5 Combine like terms: -6.5 + -2.5 = -9 x = -9 Simplifying x = -9Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, -9}
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