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Simplifying -0.25x2 + 26.50x + -142.25 = 0 Reorder the terms: -142.25 + 26.50x + -0.25x2 = 0 Solving -142.25 + 26.50x + -0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. 569 + -106x + x2 = 0 Move the constant term to the right: Add '-569' to each side of the equation. 569 + -106x + -569 + x2 = 0 + -569 Reorder the terms: 569 + -569 + -106x + x2 = 0 + -569 Combine like terms: 569 + -569 = 0 0 + -106x + x2 = 0 + -569 -106x + x2 = 0 + -569 Combine like terms: 0 + -569 = -569 -106x + x2 = -569 The x term is -106x. Take half its coefficient (-53). Square it (2809) and add it to both sides. Add '2809' to each side of the equation. -106x + 2809 + x2 = -569 + 2809 Reorder the terms: 2809 + -106x + x2 = -569 + 2809 Combine like terms: -569 + 2809 = 2240 2809 + -106x + x2 = 2240 Factor a perfect square on the left side: (x + -53)(x + -53) = 2240 Calculate the square root of the right side: 47.328638265 Break this problem into two subproblems by setting (x + -53) equal to 47.328638265 and -47.328638265.Subproblem 1
x + -53 = 47.328638265 Simplifying x + -53 = 47.328638265 Reorder the terms: -53 + x = 47.328638265 Solving -53 + x = 47.328638265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '53' to each side of the equation. -53 + 53 + x = 47.328638265 + 53 Combine like terms: -53 + 53 = 0 0 + x = 47.328638265 + 53 x = 47.328638265 + 53 Combine like terms: 47.328638265 + 53 = 100.328638265 x = 100.328638265 Simplifying x = 100.328638265Subproblem 2
x + -53 = -47.328638265 Simplifying x + -53 = -47.328638265 Reorder the terms: -53 + x = -47.328638265 Solving -53 + x = -47.328638265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '53' to each side of the equation. -53 + 53 + x = -47.328638265 + 53 Combine like terms: -53 + 53 = 0 0 + x = -47.328638265 + 53 x = -47.328638265 + 53 Combine like terms: -47.328638265 + 53 = 5.671361735 x = 5.671361735 Simplifying x = 5.671361735Solution
The solution to the problem is based on the solutions from the subproblems. x = {100.328638265, 5.671361735}
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