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Simplifying -0.5x2 + x + 12 = 9.86 Reorder the terms: 12 + x + -0.5x2 = 9.86 Solving 12 + x + -0.5x2 = 9.86 Solving for variable 'x'. Reorder the terms: 12 + -9.86 + x + -0.5x2 = 9.86 + -9.86 Combine like terms: 12 + -9.86 = 2.14 2.14 + x + -0.5x2 = 9.86 + -9.86 Combine like terms: 9.86 + -9.86 = 0.00 2.14 + x + -0.5x2 = 0.00 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -4.28 + -2x + x2 = 0.0 Move the constant term to the right: Add '4.28' to each side of the equation. -4.28 + -2x + 4.28 + x2 = 0.0 + 4.28 Reorder the terms: -4.28 + 4.28 + -2x + x2 = 0.0 + 4.28 Combine like terms: -4.28 + 4.28 = 0.00 0.00 + -2x + x2 = 0.0 + 4.28 -2x + x2 = 0.0 + 4.28 Combine like terms: 0.0 + 4.28 = 4.28 -2x + x2 = 4.28 The x term is x. 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. -2x + 0.25 + x2 = 4.28 + 0.25 Reorder the terms: 0.25 + -2x + x2 = 4.28 + 0.25 Combine like terms: 4.28 + 0.25 = 4.53 0.25 + -2x + x2 = 4.53 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4.53 Calculate the square root of the right side: 2.128379665 Break this problem into two subproblems by setting (x + 0.5) equal to 2.128379665 and -2.128379665.Subproblem 1
x + 0.5 = 2.128379665 Simplifying x + 0.5 = 2.128379665 Reorder the terms: 0.5 + x = 2.128379665 Solving 0.5 + x = 2.128379665 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 = 2.128379665 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.128379665 + -0.5 x = 2.128379665 + -0.5 Combine like terms: 2.128379665 + -0.5 = 1.628379665 x = 1.628379665 Simplifying x = 1.628379665Subproblem 2
x + 0.5 = -2.128379665 Simplifying x + 0.5 = -2.128379665 Reorder the terms: 0.5 + x = -2.128379665 Solving 0.5 + x = -2.128379665 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 = -2.128379665 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.128379665 + -0.5 x = -2.128379665 + -0.5 Combine like terms: -2.128379665 + -0.5 = -2.628379665 x = -2.628379665 Simplifying x = -2.628379665Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.628379665, -2.628379665}
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