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Simplifying (4.905x2) + 8x + -40 = 0 Reorder the terms: -40 + 8x + (4.905x2) = 0 Solving -40 + 8x + (4.905x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -8.154943935 + 1.630988787x + x2 = 0 Move the constant term to the right: Add '8.154943935' to each side of the equation. -8.154943935 + 1.630988787x + 8.154943935 + x2 = 0 + 8.154943935 Reorder the terms: -8.154943935 + 8.154943935 + 1.630988787x + x2 = 0 + 8.154943935 Combine like terms: -8.154943935 + 8.154943935 = 0.000000000 0.000000000 + 1.630988787x + x2 = 0 + 8.154943935 1.630988787x + x2 = 0 + 8.154943935 Combine like terms: 0 + 8.154943935 = 8.154943935 1.630988787x + x2 = 8.154943935 The x term is 1.630988787x. Take half its coefficient (0.8154943935). Square it (0.6650311058) and add it to both sides. Add '0.6650311058' to each side of the equation. 1.630988787x + 0.6650311058 + x2 = 8.154943935 + 0.6650311058 Reorder the terms: 0.6650311058 + 1.630988787x + x2 = 8.154943935 + 0.6650311058 Combine like terms: 8.154943935 + 0.6650311058 = 8.8199750408 0.6650311058 + 1.630988787x + x2 = 8.8199750408 Factor a perfect square on the left side: ((x) + 0.8154943935)((x) + 0.8154943935) = 8.8199750408 Calculate the square root of the right side: 2.969844279 Break this problem into two subproblems by setting ((x) + 0.8154943935) equal to 2.969844279 and -2.969844279.Subproblem 1
(x) + 0.8154943935 = 2.969844279 Simplifying (x) + 0.8154943935 = 2.969844279 x + 0.8154943935 = 2.969844279 Reorder the terms: 0.8154943935 + x = 2.969844279 Solving 0.8154943935 + x = 2.969844279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8154943935' to each side of the equation. 0.8154943935 + -0.8154943935 + x = 2.969844279 + -0.8154943935 Combine like terms: 0.8154943935 + -0.8154943935 = 0.0000000000 0.0000000000 + x = 2.969844279 + -0.8154943935 x = 2.969844279 + -0.8154943935 Combine like terms: 2.969844279 + -0.8154943935 = 2.1543498855 x = 2.1543498855 Simplifying x = 2.1543498855Subproblem 2
(x) + 0.8154943935 = -2.969844279 Simplifying (x) + 0.8154943935 = -2.969844279 x + 0.8154943935 = -2.969844279 Reorder the terms: 0.8154943935 + x = -2.969844279 Solving 0.8154943935 + x = -2.969844279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8154943935' to each side of the equation. 0.8154943935 + -0.8154943935 + x = -2.969844279 + -0.8154943935 Combine like terms: 0.8154943935 + -0.8154943935 = 0.0000000000 0.0000000000 + x = -2.969844279 + -0.8154943935 x = -2.969844279 + -0.8154943935 Combine like terms: -2.969844279 + -0.8154943935 = -3.7853386725 x = -3.7853386725 Simplifying x = -3.7853386725Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1543498855, -3.7853386725}
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