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Simplifying -0.5x2 + -10x + 12 = 0 Reorder the terms: 12 + -10x + -0.5x2 = 0 Solving 12 + -10x + -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'. -24 + 20x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 20x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 20x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 20x + x2 = 0 + 24 20x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 20x + x2 = 24 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 24 + 100 Reorder the terms: 100 + 20x + x2 = 24 + 100 Combine like terms: 24 + 100 = 124 100 + 20x + x2 = 124 Factor a perfect square on the left side: (x + 10)(x + 10) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (x + 10) equal to 11.135528726 and -11.135528726.Subproblem 1
x + 10 = 11.135528726 Simplifying x + 10 = 11.135528726 Reorder the terms: 10 + x = 11.135528726 Solving 10 + x = 11.135528726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 11.135528726 + -10 Combine like terms: 10 + -10 = 0 0 + x = 11.135528726 + -10 x = 11.135528726 + -10 Combine like terms: 11.135528726 + -10 = 1.135528726 x = 1.135528726 Simplifying x = 1.135528726Subproblem 2
x + 10 = -11.135528726 Simplifying x + 10 = -11.135528726 Reorder the terms: 10 + x = -11.135528726 Solving 10 + x = -11.135528726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -11.135528726 + -10 Combine like terms: 10 + -10 = 0 0 + x = -11.135528726 + -10 x = -11.135528726 + -10 Combine like terms: -11.135528726 + -10 = -21.135528726 x = -21.135528726 Simplifying x = -21.135528726Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.135528726, -21.135528726}
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