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Simplifying 2x2 + -85x + -1500 = 0 Reorder the terms: -1500 + -85x + 2x2 = 0 Solving -1500 + -85x + 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'. -750 + -42.5x + x2 = 0 Move the constant term to the right: Add '750' to each side of the equation. -750 + -42.5x + 750 + x2 = 0 + 750 Reorder the terms: -750 + 750 + -42.5x + x2 = 0 + 750 Combine like terms: -750 + 750 = 0 0 + -42.5x + x2 = 0 + 750 -42.5x + x2 = 0 + 750 Combine like terms: 0 + 750 = 750 -42.5x + x2 = 750 The x term is -42.5x. Take half its coefficient (-21.25). Square it (451.5625) and add it to both sides. Add '451.5625' to each side of the equation. -42.5x + 451.5625 + x2 = 750 + 451.5625 Reorder the terms: 451.5625 + -42.5x + x2 = 750 + 451.5625 Combine like terms: 750 + 451.5625 = 1201.5625 451.5625 + -42.5x + x2 = 1201.5625 Factor a perfect square on the left side: (x + -21.25)(x + -21.25) = 1201.5625 Calculate the square root of the right side: 34.66356156 Break this problem into two subproblems by setting (x + -21.25) equal to 34.66356156 and -34.66356156.Subproblem 1
x + -21.25 = 34.66356156 Simplifying x + -21.25 = 34.66356156 Reorder the terms: -21.25 + x = 34.66356156 Solving -21.25 + x = 34.66356156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21.25' to each side of the equation. -21.25 + 21.25 + x = 34.66356156 + 21.25 Combine like terms: -21.25 + 21.25 = 0.00 0.00 + x = 34.66356156 + 21.25 x = 34.66356156 + 21.25 Combine like terms: 34.66356156 + 21.25 = 55.91356156 x = 55.91356156 Simplifying x = 55.91356156Subproblem 2
x + -21.25 = -34.66356156 Simplifying x + -21.25 = -34.66356156 Reorder the terms: -21.25 + x = -34.66356156 Solving -21.25 + x = -34.66356156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21.25' to each side of the equation. -21.25 + 21.25 + x = -34.66356156 + 21.25 Combine like terms: -21.25 + 21.25 = 0.00 0.00 + x = -34.66356156 + 21.25 x = -34.66356156 + 21.25 Combine like terms: -34.66356156 + 21.25 = -13.41356156 x = -13.41356156 Simplifying x = -13.41356156Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.91356156, -13.41356156}
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