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Simplifying 2x2 + -45x + 8 = 0 Reorder the terms: 8 + -45x + 2x2 = 0 Solving 8 + -45x + 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'. 4 + -22.5x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -22.5x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -22.5x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -22.5x + x2 = 0 + -4 -22.5x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -22.5x + x2 = -4 The x term is -22.5x. Take half its coefficient (-11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. -22.5x + 126.5625 + x2 = -4 + 126.5625 Reorder the terms: 126.5625 + -22.5x + x2 = -4 + 126.5625 Combine like terms: -4 + 126.5625 = 122.5625 126.5625 + -22.5x + x2 = 122.5625 Factor a perfect square on the left side: (x + -11.25)(x + -11.25) = 122.5625 Calculate the square root of the right side: 11.070794913 Break this problem into two subproblems by setting (x + -11.25) equal to 11.070794913 and -11.070794913.Subproblem 1
x + -11.25 = 11.070794913 Simplifying x + -11.25 = 11.070794913 Reorder the terms: -11.25 + x = 11.070794913 Solving -11.25 + x = 11.070794913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = 11.070794913 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = 11.070794913 + 11.25 x = 11.070794913 + 11.25 Combine like terms: 11.070794913 + 11.25 = 22.320794913 x = 22.320794913 Simplifying x = 22.320794913Subproblem 2
x + -11.25 = -11.070794913 Simplifying x + -11.25 = -11.070794913 Reorder the terms: -11.25 + x = -11.070794913 Solving -11.25 + x = -11.070794913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = -11.070794913 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = -11.070794913 + 11.25 x = -11.070794913 + 11.25 Combine like terms: -11.070794913 + 11.25 = 0.179205087 x = 0.179205087 Simplifying x = 0.179205087Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.320794913, 0.179205087}
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