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Simplifying x + -5928910x2 = 4 Solving x + -5928910x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + x + -5928910x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + x + -5928910x2 = 0 Begin completing the square. Divide all terms by -5928910 the coefficient of the squared term: Divide each side by '-5928910'. 0.0000006746602664 + -0.0000001686650666x + x2 = 0 Move the constant term to the right: Add '-0.0000006746602664' to each side of the equation. 0.0000006746602664 + -0.0000001686650666x + -0.0000006746602664 + x2 = 0 + -0.0000006746602664 Reorder the terms: 0.0000006746602664 + -0.0000006746602664 + -0.0000001686650666x + x2 = 0 + -0.0000006746602664 Combine like terms: 0.0000006746602664 + -0.0000006746602664 = 0.0000000000000000 0.0000000000000000 + -0.0000001686650666x + x2 = 0 + -0.0000006746602664 -0.0000001686650666x + x2 = 0 + -0.0000006746602664 Combine like terms: 0 + -0.0000006746602664 = -0.0000006746602664 -0.0000001686650666x + x2 = -0.0000006746602664 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.0000001686650666x + 0.25 + x2 = -0.0000006746602664 + 0.25 Reorder the terms: 0.25 + -0.0000001686650666x + x2 = -0.0000006746602664 + 0.25 Combine like terms: -0.0000006746602664 + 0.25 = 0.2499993253397336 0.25 + -0.0000001686650666x + x2 = 0.2499993253397336 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.2499993253397336 Calculate the square root of the right side: 0.499999325 Break this problem into two subproblems by setting (x + 0.5) equal to 0.499999325 and -0.499999325.Subproblem 1
x + 0.5 = 0.499999325 Simplifying x + 0.5 = 0.499999325 Reorder the terms: 0.5 + x = 0.499999325 Solving 0.5 + x = 0.499999325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.499999325 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.499999325 + -0.5 x = 0.499999325 + -0.5 Combine like terms: 0.499999325 + -0.5 = -0.000000675 x = -0.000000675 Simplifying x = -0.000000675Subproblem 2
x + 0.5 = -0.499999325 Simplifying x + 0.5 = -0.499999325 Reorder the terms: 0.5 + x = -0.499999325 Solving 0.5 + x = -0.499999325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.499999325 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.499999325 + -0.5 x = -0.499999325 + -0.5 Combine like terms: -0.499999325 + -0.5 = -0.999999325 x = -0.999999325 Simplifying x = -0.999999325Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.000000675, -0.999999325}
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