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Simplifying -0.25x2 + 26.50x + -702.25 = 0 Reorder the terms: -702.25 + 26.50x + -0.25x2 = 0 Solving -702.25 + 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'. 2809 + -106x + x2 = 0 Move the constant term to the right: Add '-2809' to each side of the equation. 2809 + -106x + -2809 + x2 = 0 + -2809 Reorder the terms: 2809 + -2809 + -106x + x2 = 0 + -2809 Combine like terms: 2809 + -2809 = 0 0 + -106x + x2 = 0 + -2809 -106x + x2 = 0 + -2809 Combine like terms: 0 + -2809 = -2809 -106x + x2 = -2809 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 = -2809 + 2809 Reorder the terms: 2809 + -106x + x2 = -2809 + 2809 Combine like terms: -2809 + 2809 = 0 2809 + -106x + x2 = 0 Factor a perfect square on the left side: (x + -53)(x + -53) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x + -53) equal to 0 and 0.Subproblem 1
x + -53 = 0 Simplifying x + -53 = 0 Reorder the terms: -53 + x = 0 Solving -53 + x = 0 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 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + x = 0 + 53 x = 0 + 53 Combine like terms: 0 + 53 = 53 x = 53 Simplifying x = 53Subproblem 2
x + -53 = 0 Simplifying x + -53 = 0 Reorder the terms: -53 + x = 0 Solving -53 + x = 0 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 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + x = 0 + 53 x = 0 + 53 Combine like terms: 0 + 53 = 53 x = 53 Simplifying x = 53Solution
The solution to the problem is based on the solutions from the subproblems. x = {53, 53}
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