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Simplifying x2 + 65x + -186 = 0 Reorder the terms: -186 + 65x + x2 = 0 Solving -186 + 65x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '186' to each side of the equation. -186 + 65x + 186 + x2 = 0 + 186 Reorder the terms: -186 + 186 + 65x + x2 = 0 + 186 Combine like terms: -186 + 186 = 0 0 + 65x + x2 = 0 + 186 65x + x2 = 0 + 186 Combine like terms: 0 + 186 = 186 65x + x2 = 186 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 = 186 + 1056.25 Reorder the terms: 1056.25 + 65x + x2 = 186 + 1056.25 Combine like terms: 186 + 1056.25 = 1242.25 1056.25 + 65x + x2 = 1242.25 Factor a perfect square on the left side: (x + 32.5)(x + 32.5) = 1242.25 Calculate the square root of the right side: 35.245567097 Break this problem into two subproblems by setting (x + 32.5) equal to 35.245567097 and -35.245567097.Subproblem 1
x + 32.5 = 35.245567097 Simplifying x + 32.5 = 35.245567097 Reorder the terms: 32.5 + x = 35.245567097 Solving 32.5 + x = 35.245567097 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 = 35.245567097 + -32.5 Combine like terms: 32.5 + -32.5 = 0.0 0.0 + x = 35.245567097 + -32.5 x = 35.245567097 + -32.5 Combine like terms: 35.245567097 + -32.5 = 2.745567097 x = 2.745567097 Simplifying x = 2.745567097Subproblem 2
x + 32.5 = -35.245567097 Simplifying x + 32.5 = -35.245567097 Reorder the terms: 32.5 + x = -35.245567097 Solving 32.5 + x = -35.245567097 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 = -35.245567097 + -32.5 Combine like terms: 32.5 + -32.5 = 0.0 0.0 + x = -35.245567097 + -32.5 x = -35.245567097 + -32.5 Combine like terms: -35.245567097 + -32.5 = -67.745567097 x = -67.745567097 Simplifying x = -67.745567097Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.745567097, -67.745567097}
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