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Simplifying -0.5x2 + 36x + -310 = 0 Reorder the terms: -310 + 36x + -0.5x2 = 0 Solving -310 + 36x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 620 + -72x + x2 = 0 Move the constant term to the right: Add '-620' to each side of the equation. 620 + -72x + -620 + x2 = 0 + -620 Reorder the terms: 620 + -620 + -72x + x2 = 0 + -620 Combine like terms: 620 + -620 = 0 0 + -72x + x2 = 0 + -620 -72x + x2 = 0 + -620 Combine like terms: 0 + -620 = -620 -72x + x2 = -620 The x term is -72x. Take half its coefficient (-36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. -72x + 1296 + x2 = -620 + 1296 Reorder the terms: 1296 + -72x + x2 = -620 + 1296 Combine like terms: -620 + 1296 = 676 1296 + -72x + x2 = 676 Factor a perfect square on the left side: (x + -36)(x + -36) = 676 Calculate the square root of the right side: 26 Break this problem into two subproblems by setting (x + -36) equal to 26 and -26.Subproblem 1
x + -36 = 26 Simplifying x + -36 = 26 Reorder the terms: -36 + x = 26 Solving -36 + x = 26 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = 26 + 36 Combine like terms: -36 + 36 = 0 0 + x = 26 + 36 x = 26 + 36 Combine like terms: 26 + 36 = 62 x = 62 Simplifying x = 62Subproblem 2
x + -36 = -26 Simplifying x + -36 = -26 Reorder the terms: -36 + x = -26 Solving -36 + x = -26 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = -26 + 36 Combine like terms: -36 + 36 = 0 0 + x = -26 + 36 x = -26 + 36 Combine like terms: -26 + 36 = 10 x = 10 Simplifying x = 10Solution
The solution to the problem is based on the solutions from the subproblems. x = {62, 10}
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