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Simplifying 2x2 + -60x + 600 = 762.50 Reorder the terms: 600 + -60x + 2x2 = 762.50 Solving 600 + -60x + 2x2 = 762.50 Solving for variable 'x'. Reorder the terms: 600 + -762.50 + -60x + 2x2 = 762.50 + -762.50 Combine like terms: 600 + -762.50 = -162.5 -162.5 + -60x + 2x2 = 762.50 + -762.50 Combine like terms: 762.50 + -762.50 = 0.00 -162.5 + -60x + 2x2 = 0.00 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -81.25 + -30x + x2 = 0.00 Move the constant term to the right: Add '81.25' to each side of the equation. -81.25 + -30x + 81.25 + x2 = 0.00 + 81.25 Reorder the terms: -81.25 + 81.25 + -30x + x2 = 0.00 + 81.25 Combine like terms: -81.25 + 81.25 = 0.00 0.00 + -30x + x2 = 0.00 + 81.25 -30x + x2 = 0.00 + 81.25 Combine like terms: 0.00 + 81.25 = 81.25 -30x + x2 = 81.25 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = 81.25 + 225 Reorder the terms: 225 + -30x + x2 = 81.25 + 225 Combine like terms: 81.25 + 225 = 306.25 225 + -30x + x2 = 306.25 Factor a perfect square on the left side: (x + -15)(x + -15) = 306.25 Calculate the square root of the right side: 17.5 Break this problem into two subproblems by setting (x + -15) equal to 17.5 and -17.5.Subproblem 1
x + -15 = 17.5 Simplifying x + -15 = 17.5 Reorder the terms: -15 + x = 17.5 Solving -15 + x = 17.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 17.5 + 15 Combine like terms: -15 + 15 = 0 0 + x = 17.5 + 15 x = 17.5 + 15 Combine like terms: 17.5 + 15 = 32.5 x = 32.5 Simplifying x = 32.5Subproblem 2
x + -15 = -17.5 Simplifying x + -15 = -17.5 Reorder the terms: -15 + x = -17.5 Solving -15 + x = -17.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -17.5 + 15 Combine like terms: -15 + 15 = 0 0 + x = -17.5 + 15 x = -17.5 + 15 Combine like terms: -17.5 + 15 = -2.5 x = -2.5 Simplifying x = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.5, -2.5}
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