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Simplifying 0.5x2 + -0.5x + -10 = 0 Reorder the terms: -10 + -0.5x + 0.5x2 = 0 Solving -10 + -0.5x + 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'. -20 + -1x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -1x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -1x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -1x + x2 = 0 + 20 -1x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -1x + x2 = 20 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 20 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 20 + 0.25 Combine like terms: 20 + 0.25 = 20.25 0.25 + -1x + x2 = 20.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 20.25 Calculate the square root of the right side: 4.5 Break this problem into two subproblems by setting (x + -0.5) equal to 4.5 and -4.5.Subproblem 1
x + -0.5 = 4.5 Simplifying x + -0.5 = 4.5 Reorder the terms: -0.5 + x = 4.5 Solving -0.5 + x = 4.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 4.5 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 4.5 + 0.5 x = 4.5 + 0.5 Combine like terms: 4.5 + 0.5 = 5 x = 5 Simplifying x = 5Subproblem 2
x + -0.5 = -4.5 Simplifying x + -0.5 = -4.5 Reorder the terms: -0.5 + x = -4.5 Solving -0.5 + x = -4.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -4.5 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -4.5 + 0.5 x = -4.5 + 0.5 Combine like terms: -4.5 + 0.5 = -4 x = -4 Simplifying x = -4Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, -4}
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