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Simplifying 18x2 + 15x + -22 = 0 Reorder the terms: -22 + 15x + 18x2 = 0 Solving -22 + 15x + 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'. -1.222222222 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '1.222222222' to each side of the equation. -1.222222222 + 0.8333333333x + 1.222222222 + x2 = 0 + 1.222222222 Reorder the terms: -1.222222222 + 1.222222222 + 0.8333333333x + x2 = 0 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + 0.8333333333x + x2 = 0 + 1.222222222 0.8333333333x + x2 = 0 + 1.222222222 Combine like terms: 0 + 1.222222222 = 1.222222222 0.8333333333x + x2 = 1.222222222 The x term is 0.8333333333x. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333x + 0.1736111111 + x2 = 1.222222222 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = 1.222222222 + 0.1736111111 Combine like terms: 1.222222222 + 0.1736111111 = 1.3958333331 0.1736111111 + 0.8333333333x + x2 = 1.3958333331 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = 1.3958333331 Calculate the square root of the right side: 1.181453906 Break this problem into two subproblems by setting (x + 0.4166666667) equal to 1.181453906 and -1.181453906.Subproblem 1
x + 0.4166666667 = 1.181453906 Simplifying x + 0.4166666667 = 1.181453906 Reorder the terms: 0.4166666667 + x = 1.181453906 Solving 0.4166666667 + x = 1.181453906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = 1.181453906 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 1.181453906 + -0.4166666667 x = 1.181453906 + -0.4166666667 Combine like terms: 1.181453906 + -0.4166666667 = 0.7647872393 x = 0.7647872393 Simplifying x = 0.7647872393Subproblem 2
x + 0.4166666667 = -1.181453906 Simplifying x + 0.4166666667 = -1.181453906 Reorder the terms: 0.4166666667 + x = -1.181453906 Solving 0.4166666667 + x = -1.181453906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = -1.181453906 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -1.181453906 + -0.4166666667 x = -1.181453906 + -0.4166666667 Combine like terms: -1.181453906 + -0.4166666667 = -1.5981205727 x = -1.5981205727 Simplifying x = -1.5981205727Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7647872393, -1.5981205727}
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