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Simplifying 65x + -1x2 + -800 = 0 Reorder the terms: -800 + 65x + -1x2 = 0 Solving -800 + 65x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 800 + -65x + x2 = 0 Move the constant term to the right: Add '-800' to each side of the equation. 800 + -65x + -800 + x2 = 0 + -800 Reorder the terms: 800 + -800 + -65x + x2 = 0 + -800 Combine like terms: 800 + -800 = 0 0 + -65x + x2 = 0 + -800 -65x + x2 = 0 + -800 Combine like terms: 0 + -800 = -800 -65x + x2 = -800 The x term is -65x. Take half its coefficient (-32.5). Square it (1056.25) and add it to both sides. Add '1056.25' to each side of the equation. -65x + 1056.25 + x2 = -800 + 1056.25 Reorder the terms: 1056.25 + -65x + x2 = -800 + 1056.25 Combine like terms: -800 + 1056.25 = 256.25 1056.25 + -65x + x2 = 256.25 Factor a perfect square on the left side: (x + -32.5)(x + -32.5) = 256.25 Calculate the square root of the right side: 16.007810594 Break this problem into two subproblems by setting (x + -32.5) equal to 16.007810594 and -16.007810594.Subproblem 1
x + -32.5 = 16.007810594 Simplifying x + -32.5 = 16.007810594 Reorder the terms: -32.5 + x = 16.007810594 Solving -32.5 + x = 16.007810594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32.5' to each side of the equation. -32.5 + 32.5 + x = 16.007810594 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + x = 16.007810594 + 32.5 x = 16.007810594 + 32.5 Combine like terms: 16.007810594 + 32.5 = 48.507810594 x = 48.507810594 Simplifying x = 48.507810594Subproblem 2
x + -32.5 = -16.007810594 Simplifying x + -32.5 = -16.007810594 Reorder the terms: -32.5 + x = -16.007810594 Solving -32.5 + x = -16.007810594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32.5' to each side of the equation. -32.5 + 32.5 + x = -16.007810594 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + x = -16.007810594 + 32.5 x = -16.007810594 + 32.5 Combine like terms: -16.007810594 + 32.5 = 16.492189406 x = 16.492189406 Simplifying x = 16.492189406Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.507810594, 16.492189406}
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