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Simplifying x2 + 615x + -53400 = 0 Reorder the terms: -53400 + 615x + x2 = 0 Solving -53400 + 615x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '53400' to each side of the equation. -53400 + 615x + 53400 + x2 = 0 + 53400 Reorder the terms: -53400 + 53400 + 615x + x2 = 0 + 53400 Combine like terms: -53400 + 53400 = 0 0 + 615x + x2 = 0 + 53400 615x + x2 = 0 + 53400 Combine like terms: 0 + 53400 = 53400 615x + x2 = 53400 The x term is 615x. Take half its coefficient (307.5). Square it (94556.25) and add it to both sides. Add '94556.25' to each side of the equation. 615x + 94556.25 + x2 = 53400 + 94556.25 Reorder the terms: 94556.25 + 615x + x2 = 53400 + 94556.25 Combine like terms: 53400 + 94556.25 = 147956.25 94556.25 + 615x + x2 = 147956.25 Factor a perfect square on the left side: (x + 307.5)(x + 307.5) = 147956.25 Calculate the square root of the right side: 384.650815676 Break this problem into two subproblems by setting (x + 307.5) equal to 384.650815676 and -384.650815676.Subproblem 1
x + 307.5 = 384.650815676 Simplifying x + 307.5 = 384.650815676 Reorder the terms: 307.5 + x = 384.650815676 Solving 307.5 + x = 384.650815676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-307.5' to each side of the equation. 307.5 + -307.5 + x = 384.650815676 + -307.5 Combine like terms: 307.5 + -307.5 = 0.0 0.0 + x = 384.650815676 + -307.5 x = 384.650815676 + -307.5 Combine like terms: 384.650815676 + -307.5 = 77.150815676 x = 77.150815676 Simplifying x = 77.150815676Subproblem 2
x + 307.5 = -384.650815676 Simplifying x + 307.5 = -384.650815676 Reorder the terms: 307.5 + x = -384.650815676 Solving 307.5 + x = -384.650815676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-307.5' to each side of the equation. 307.5 + -307.5 + x = -384.650815676 + -307.5 Combine like terms: 307.5 + -307.5 = 0.0 0.0 + x = -384.650815676 + -307.5 x = -384.650815676 + -307.5 Combine like terms: -384.650815676 + -307.5 = -692.150815676 x = -692.150815676 Simplifying x = -692.150815676Solution
The solution to the problem is based on the solutions from the subproblems. x = {77.150815676, -692.150815676}
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