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Simplifying 0 = 65x + -1x2 + -156 Reorder the terms: 0 = -156 + 65x + -1x2 Solving 0 = -156 + 65x + -1x2 Solving for variable 'x'. Combine like terms: 0 + 156 = 156 156 + -65x + x2 = -156 + 65x + -1x2 + 156 + -65x + x2 Reorder the terms: 156 + -65x + x2 = -156 + 156 + 65x + -65x + -1x2 + x2 Combine like terms: -156 + 156 = 0 156 + -65x + x2 = 0 + 65x + -65x + -1x2 + x2 156 + -65x + x2 = 65x + -65x + -1x2 + x2 Combine like terms: 65x + -65x = 0 156 + -65x + x2 = 0 + -1x2 + x2 156 + -65x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 156 + -65x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-156' to each side of the equation. 156 + -65x + -156 + x2 = 0 + -156 Reorder the terms: 156 + -156 + -65x + x2 = 0 + -156 Combine like terms: 156 + -156 = 0 0 + -65x + x2 = 0 + -156 -65x + x2 = 0 + -156 Combine like terms: 0 + -156 = -156 -65x + x2 = -156 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 = -156 + 1056.25 Reorder the terms: 1056.25 + -65x + x2 = -156 + 1056.25 Combine like terms: -156 + 1056.25 = 900.25 1056.25 + -65x + x2 = 900.25 Factor a perfect square on the left side: (x + -32.5)(x + -32.5) = 900.25 Calculate the square root of the right side: 30.004166377 Break this problem into two subproblems by setting (x + -32.5) equal to 30.004166377 and -30.004166377.Subproblem 1
x + -32.5 = 30.004166377 Simplifying x + -32.5 = 30.004166377 Reorder the terms: -32.5 + x = 30.004166377 Solving -32.5 + x = 30.004166377 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 = 30.004166377 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + x = 30.004166377 + 32.5 x = 30.004166377 + 32.5 Combine like terms: 30.004166377 + 32.5 = 62.504166377 x = 62.504166377 Simplifying x = 62.504166377Subproblem 2
x + -32.5 = -30.004166377 Simplifying x + -32.5 = -30.004166377 Reorder the terms: -32.5 + x = -30.004166377 Solving -32.5 + x = -30.004166377 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 = -30.004166377 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + x = -30.004166377 + 32.5 x = -30.004166377 + 32.5 Combine like terms: -30.004166377 + 32.5 = 2.495833623 x = 2.495833623 Simplifying x = 2.495833623Solution
The solution to the problem is based on the solutions from the subproblems. x = {62.504166377, 2.495833623}
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