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Simplifying (0.09x2) + (0.1x) = 2.9 Reorder the terms: (0.1x) + (0.09x2) = 2.9 Solving (0.1x) + (0.09x2) = 2.9 Solving for variable 'x'. Reorder the terms: -2.9 + (0.1x) + (0.09x2) = 2.9 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 -2.9 + (0.1x) + (0.09x2) = 0.0 Begin completing the square. Divide all terms by 0.09 the coefficient of the squared term: Divide each side by '0.09'. -32.22222222 + (1.111111111x) + x2 = 0 Move the constant term to the right: Add '32.22222222' to each side of the equation. -32.22222222 + (1.111111111x) + 32.22222222 + x2 = 0 + 32.22222222 Reorder the terms: -32.22222222 + 32.22222222 + (1.111111111x) + x2 = 0 + 32.22222222 Combine like terms: -32.22222222 + 32.22222222 = 0.00000000 0.00000000 + (1.111111111x) + x2 = 0 + 32.22222222 (1.111111111x) + x2 = 0 + 32.22222222 Combine like terms: 0 + 32.22222222 = 32.22222222 (1.111111111x) + x2 = 32.22222222 The x term is (1.111111111x). Take half its coefficient (0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. (1.111111111x) + 0.3086419752 + x2 = 32.22222222 + 0.3086419752 Reorder the terms: 0.3086419752 + (1.111111111x) + x2 = 32.22222222 + 0.3086419752 Combine like terms: 32.22222222 + 0.3086419752 = 32.5308641952 0.3086419752 + (1.111111111x) + x2 = 32.5308641952 Factor a perfect square on the left side: ((x) + 0.5555555555)((x) + 0.5555555555) = 32.5308641952 Calculate the square root of the right side: 5.703583452 Break this problem into two subproblems by setting ((x) + 0.5555555555) equal to 5.703583452 and -5.703583452.Subproblem 1
(x) + 0.5555555555 = 5.703583452 Simplifying (x) + 0.5555555555 = 5.703583452 x + 0.5555555555 = 5.703583452 Reorder the terms: 0.5555555555 + x = 5.703583452 Solving 0.5555555555 + x = 5.703583452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = 5.703583452 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = 5.703583452 + -0.5555555555 x = 5.703583452 + -0.5555555555 Combine like terms: 5.703583452 + -0.5555555555 = 5.1480278965 x = 5.1480278965 Simplifying x = 5.1480278965Subproblem 2
(x) + 0.5555555555 = -5.703583452 Simplifying (x) + 0.5555555555 = -5.703583452 x + 0.5555555555 = -5.703583452 Reorder the terms: 0.5555555555 + x = -5.703583452 Solving 0.5555555555 + x = -5.703583452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = -5.703583452 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = -5.703583452 + -0.5555555555 x = -5.703583452 + -0.5555555555 Combine like terms: -5.703583452 + -0.5555555555 = -6.2591390075 x = -6.2591390075 Simplifying x = -6.2591390075Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.1480278965, -6.2591390075}
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