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Simplifying 12 + x = 0 + 92x2 Remove the zero: 12 + x = 92x2 Solving 12 + x = 92x2 Solving for variable 'x'. Combine like terms: 92x2 + -92x2 = 0 12 + x + -92x2 = 0 Begin completing the square. Divide all terms by -92 the coefficient of the squared term: Divide each side by '-92'. -0.1304347826 + -0.01086956522x + x2 = 0 Move the constant term to the right: Add '0.1304347826' to each side of the equation. -0.1304347826 + -0.01086956522x + 0.1304347826 + x2 = 0 + 0.1304347826 Reorder the terms: -0.1304347826 + 0.1304347826 + -0.01086956522x + x2 = 0 + 0.1304347826 Combine like terms: -0.1304347826 + 0.1304347826 = 0.0000000000 0.0000000000 + -0.01086956522x + x2 = 0 + 0.1304347826 -0.01086956522x + x2 = 0 + 0.1304347826 Combine like terms: 0 + 0.1304347826 = 0.1304347826 -0.01086956522x + x2 = 0.1304347826 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. -0.01086956522x + 0.25 + x2 = 0.1304347826 + 0.25 Reorder the terms: 0.25 + -0.01086956522x + x2 = 0.1304347826 + 0.25 Combine like terms: 0.1304347826 + 0.25 = 0.3804347826 0.25 + -0.01086956522x + x2 = 0.3804347826 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.3804347826 Calculate the square root of the right side: 0.616793955 Break this problem into two subproblems by setting (x + 0.5) equal to 0.616793955 and -0.616793955.Subproblem 1
x + 0.5 = 0.616793955 Simplifying x + 0.5 = 0.616793955 Reorder the terms: 0.5 + x = 0.616793955 Solving 0.5 + x = 0.616793955 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 = 0.616793955 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.616793955 + -0.5 x = 0.616793955 + -0.5 Combine like terms: 0.616793955 + -0.5 = 0.116793955 x = 0.116793955 Simplifying x = 0.116793955Subproblem 2
x + 0.5 = -0.616793955 Simplifying x + 0.5 = -0.616793955 Reorder the terms: 0.5 + x = -0.616793955 Solving 0.5 + x = -0.616793955 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 = -0.616793955 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.616793955 + -0.5 x = -0.616793955 + -0.5 Combine like terms: -0.616793955 + -0.5 = -1.116793955 x = -1.116793955 Simplifying x = -1.116793955Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.116793955, -1.116793955}
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