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Simplifying 0 = x2 + 155x + -360 Reorder the terms: 0 = -360 + 155x + x2 Solving 0 = -360 + 155x + x2 Solving for variable 'x'. Combine like terms: 0 + 360 = 360 360 + -155x + -1x2 = -360 + 155x + x2 + 360 + -155x + -1x2 Reorder the terms: 360 + -155x + -1x2 = -360 + 360 + 155x + -155x + x2 + -1x2 Combine like terms: -360 + 360 = 0 360 + -155x + -1x2 = 0 + 155x + -155x + x2 + -1x2 360 + -155x + -1x2 = 155x + -155x + x2 + -1x2 Combine like terms: 155x + -155x = 0 360 + -155x + -1x2 = 0 + x2 + -1x2 360 + -155x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 360 + -155x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -360 + 155x + x2 = 0 Move the constant term to the right: Add '360' to each side of the equation. -360 + 155x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + 155x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 155x + x2 = 0 + 360 155x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 155x + x2 = 360 The x term is 155x. Take half its coefficient (77.5). Square it (6006.25) and add it to both sides. Add '6006.25' to each side of the equation. 155x + 6006.25 + x2 = 360 + 6006.25 Reorder the terms: 6006.25 + 155x + x2 = 360 + 6006.25 Combine like terms: 360 + 6006.25 = 6366.25 6006.25 + 155x + x2 = 6366.25 Factor a perfect square on the left side: (x + 77.5)(x + 77.5) = 6366.25 Calculate the square root of the right side: 79.788783673 Break this problem into two subproblems by setting (x + 77.5) equal to 79.788783673 and -79.788783673.Subproblem 1
x + 77.5 = 79.788783673 Simplifying x + 77.5 = 79.788783673 Reorder the terms: 77.5 + x = 79.788783673 Solving 77.5 + x = 79.788783673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-77.5' to each side of the equation. 77.5 + -77.5 + x = 79.788783673 + -77.5 Combine like terms: 77.5 + -77.5 = 0.0 0.0 + x = 79.788783673 + -77.5 x = 79.788783673 + -77.5 Combine like terms: 79.788783673 + -77.5 = 2.288783673 x = 2.288783673 Simplifying x = 2.288783673Subproblem 2
x + 77.5 = -79.788783673 Simplifying x + 77.5 = -79.788783673 Reorder the terms: 77.5 + x = -79.788783673 Solving 77.5 + x = -79.788783673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-77.5' to each side of the equation. 77.5 + -77.5 + x = -79.788783673 + -77.5 Combine like terms: 77.5 + -77.5 = 0.0 0.0 + x = -79.788783673 + -77.5 x = -79.788783673 + -77.5 Combine like terms: -79.788783673 + -77.5 = -157.288783673 x = -157.288783673 Simplifying x = -157.288783673Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.288783673, -157.288783673}
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