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Simplifying -1x2 + 65x + -450 = 0 Reorder the terms: -450 + 65x + -1x2 = 0 Solving -450 + 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'. 450 + -65x + x2 = 0 Move the constant term to the right: Add '-450' to each side of the equation. 450 + -65x + -450 + x2 = 0 + -450 Reorder the terms: 450 + -450 + -65x + x2 = 0 + -450 Combine like terms: 450 + -450 = 0 0 + -65x + x2 = 0 + -450 -65x + x2 = 0 + -450 Combine like terms: 0 + -450 = -450 -65x + x2 = -450 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 = -450 + 1056.25 Reorder the terms: 1056.25 + -65x + x2 = -450 + 1056.25 Combine like terms: -450 + 1056.25 = 606.25 1056.25 + -65x + x2 = 606.25 Factor a perfect square on the left side: (x + -32.5)(x + -32.5) = 606.25 Calculate the square root of the right side: 24.622144504 Break this problem into two subproblems by setting (x + -32.5) equal to 24.622144504 and -24.622144504.Subproblem 1
x + -32.5 = 24.622144504 Simplifying x + -32.5 = 24.622144504 Reorder the terms: -32.5 + x = 24.622144504 Solving -32.5 + x = 24.622144504 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 = 24.622144504 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + x = 24.622144504 + 32.5 x = 24.622144504 + 32.5 Combine like terms: 24.622144504 + 32.5 = 57.122144504 x = 57.122144504 Simplifying x = 57.122144504Subproblem 2
x + -32.5 = -24.622144504 Simplifying x + -32.5 = -24.622144504 Reorder the terms: -32.5 + x = -24.622144504 Solving -32.5 + x = -24.622144504 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 = -24.622144504 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + x = -24.622144504 + 32.5 x = -24.622144504 + 32.5 Combine like terms: -24.622144504 + 32.5 = 7.877855496 x = 7.877855496 Simplifying x = 7.877855496Solution
The solution to the problem is based on the solutions from the subproblems. x = {57.122144504, 7.877855496}
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