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Simplifying 18x2 + 36x + 13 = 0 Reorder the terms: 13 + 36x + 18x2 = 0 Solving 13 + 36x + 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'. 0.7222222222 + 2x + x2 = 0 Move the constant term to the right: Add '-0.7222222222' to each side of the equation. 0.7222222222 + 2x + -0.7222222222 + x2 = 0 + -0.7222222222 Reorder the terms: 0.7222222222 + -0.7222222222 + 2x + x2 = 0 + -0.7222222222 Combine like terms: 0.7222222222 + -0.7222222222 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + -0.7222222222 2x + x2 = 0 + -0.7222222222 Combine like terms: 0 + -0.7222222222 = -0.7222222222 2x + x2 = -0.7222222222 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.7222222222 + 1 Reorder the terms: 1 + 2x + x2 = -0.7222222222 + 1 Combine like terms: -0.7222222222 + 1 = 0.2777777778 1 + 2x + x2 = 0.2777777778 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.2777777778 Calculate the square root of the right side: 0.527046277 Break this problem into two subproblems by setting (x + 1) equal to 0.527046277 and -0.527046277.Subproblem 1
x + 1 = 0.527046277 Simplifying x + 1 = 0.527046277 Reorder the terms: 1 + x = 0.527046277 Solving 1 + x = 0.527046277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.527046277 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.527046277 + -1 x = 0.527046277 + -1 Combine like terms: 0.527046277 + -1 = -0.472953723 x = -0.472953723 Simplifying x = -0.472953723Subproblem 2
x + 1 = -0.527046277 Simplifying x + 1 = -0.527046277 Reorder the terms: 1 + x = -0.527046277 Solving 1 + x = -0.527046277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.527046277 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.527046277 + -1 x = -0.527046277 + -1 Combine like terms: -0.527046277 + -1 = -1.527046277 x = -1.527046277 Simplifying x = -1.527046277Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.472953723, -1.527046277}
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