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Simplifying x2 + -0.08658008658x + 0.0001623376 = 6 Reorder the terms: 0.0001623376 + -0.08658008658x + x2 = 6 Solving 0.0001623376 + -0.08658008658x + x2 = 6 Solving for variable 'x'. Reorder the terms: 0.0001623376 + -6 + -0.08658008658x + x2 = 6 + -6 Combine like terms: 0.0001623376 + -6 = -5.9998376624 -5.9998376624 + -0.08658008658x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -5.9998376624 + -0.08658008658x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5.9998376624' to each side of the equation. -5.9998376624 + -0.08658008658x + 5.9998376624 + x2 = 0 + 5.9998376624 Reorder the terms: -5.9998376624 + 5.9998376624 + -0.08658008658x + x2 = 0 + 5.9998376624 Combine like terms: -5.9998376624 + 5.9998376624 = 0.0000000000 0.0000000000 + -0.08658008658x + x2 = 0 + 5.9998376624 -0.08658008658x + x2 = 0 + 5.9998376624 Combine like terms: 0 + 5.9998376624 = 5.9998376624 -0.08658008658x + x2 = 5.9998376624 The x term is -0.08658008658x. Take half its coefficient (-0.04329004329). Square it (0.001874027848) and add it to both sides. Add '0.001874027848' to each side of the equation. -0.08658008658x + 0.001874027848 + x2 = 5.9998376624 + 0.001874027848 Reorder the terms: 0.001874027848 + -0.08658008658x + x2 = 5.9998376624 + 0.001874027848 Combine like terms: 5.9998376624 + 0.001874027848 = 6.001711690248 0.001874027848 + -0.08658008658x + x2 = 6.001711690248 Factor a perfect square on the left side: (x + -0.04329004329)(x + -0.04329004329) = 6.001711690248 Calculate the square root of the right side: 2.449839115 Break this problem into two subproblems by setting (x + -0.04329004329) equal to 2.449839115 and -2.449839115.Subproblem 1
x + -0.04329004329 = 2.449839115 Simplifying x + -0.04329004329 = 2.449839115 Reorder the terms: -0.04329004329 + x = 2.449839115 Solving -0.04329004329 + x = 2.449839115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04329004329' to each side of the equation. -0.04329004329 + 0.04329004329 + x = 2.449839115 + 0.04329004329 Combine like terms: -0.04329004329 + 0.04329004329 = 0.00000000000 0.00000000000 + x = 2.449839115 + 0.04329004329 x = 2.449839115 + 0.04329004329 Combine like terms: 2.449839115 + 0.04329004329 = 2.49312915829 x = 2.49312915829 Simplifying x = 2.49312915829Subproblem 2
x + -0.04329004329 = -2.449839115 Simplifying x + -0.04329004329 = -2.449839115 Reorder the terms: -0.04329004329 + x = -2.449839115 Solving -0.04329004329 + x = -2.449839115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04329004329' to each side of the equation. -0.04329004329 + 0.04329004329 + x = -2.449839115 + 0.04329004329 Combine like terms: -0.04329004329 + 0.04329004329 = 0.00000000000 0.00000000000 + x = -2.449839115 + 0.04329004329 x = -2.449839115 + 0.04329004329 Combine like terms: -2.449839115 + 0.04329004329 = -2.40654907171 x = -2.40654907171 Simplifying x = -2.40654907171Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.49312915829, -2.40654907171}
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