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Simplifying 18x2 + 45x + 2 = 0 Reorder the terms: 2 + 45x + 18x2 = 0 Solving 2 + 45x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.1111111111 + 2.5x + x2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + 2.5x + -0.1111111111 + x2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + 2.5x + x2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + 2.5x + x2 = 0 + -0.1111111111 2.5x + x2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 2.5x + x2 = -0.1111111111 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = -0.1111111111 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -0.1111111111 + 1.5625 Combine like terms: -0.1111111111 + 1.5625 = 1.4513888889 1.5625 + 2.5x + x2 = 1.4513888889 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 1.4513888889 Calculate the square root of the right side: 1.204736025 Break this problem into two subproblems by setting (x + 1.25) equal to 1.204736025 and -1.204736025.Subproblem 1
x + 1.25 = 1.204736025 Simplifying x + 1.25 = 1.204736025 Reorder the terms: 1.25 + x = 1.204736025 Solving 1.25 + x = 1.204736025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.204736025 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.204736025 + -1.25 x = 1.204736025 + -1.25 Combine like terms: 1.204736025 + -1.25 = -0.045263975 x = -0.045263975 Simplifying x = -0.045263975Subproblem 2
x + 1.25 = -1.204736025 Simplifying x + 1.25 = -1.204736025 Reorder the terms: 1.25 + x = -1.204736025 Solving 1.25 + x = -1.204736025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.204736025 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.204736025 + -1.25 x = -1.204736025 + -1.25 Combine like terms: -1.204736025 + -1.25 = -2.454736025 x = -2.454736025 Simplifying x = -2.454736025Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.045263975, -2.454736025}
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