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Simplifying -2x2 + -2x + 24.01 = 0 Reorder the terms: 24.01 + -2x + -2x2 = 0 Solving 24.01 + -2x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -12.005 + x + x2 = 0 Move the constant term to the right: Add '12.005' to each side of the equation. -12.005 + x + 12.005 + x2 = 0 + 12.005 Reorder the terms: -12.005 + 12.005 + x + x2 = 0 + 12.005 Combine like terms: -12.005 + 12.005 = 0.000 0.000 + x + x2 = 0 + 12.005 x + x2 = 0 + 12.005 Combine like terms: 0 + 12.005 = 12.005 x + x2 = 12.005 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. + 0.25 + x2 = 12.005 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 12.005 + 0.25 Combine like terms: 12.005 + 0.25 = 12.255 1.25 + x2 = 12.255 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 12.255 Calculate the square root of the right side: 3.500714213 Break this problem into two subproblems by setting (x + 0.5) equal to 3.500714213 and -3.500714213.Subproblem 1
x + 0.5 = 3.500714213 Simplifying x + 0.5 = 3.500714213 Reorder the terms: 0.5 + x = 3.500714213 Solving 0.5 + x = 3.500714213 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 = 3.500714213 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.500714213 + -0.5 x = 3.500714213 + -0.5 Combine like terms: 3.500714213 + -0.5 = 3.000714213 x = 3.000714213 Simplifying x = 3.000714213Subproblem 2
x + 0.5 = -3.500714213 Simplifying x + 0.5 = -3.500714213 Reorder the terms: 0.5 + x = -3.500714213 Solving 0.5 + x = -3.500714213 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 = -3.500714213 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.500714213 + -0.5 x = -3.500714213 + -0.5 Combine like terms: -3.500714213 + -0.5 = -4.000714213 x = -4.000714213 Simplifying x = -4.000714213Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.000714213, -4.000714213}
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