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Simplifying 9.5x2 + 3.3x + -2.7 = 0 Reorder the terms: -2.7 + 3.3x + 9.5x2 = 0 Solving -2.7 + 3.3x + 9.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9.5 the coefficient of the squared term: Divide each side by '9.5'. -0.2842105263 + 0.3473684211x + x2 = 0 Move the constant term to the right: Add '0.2842105263' to each side of the equation. -0.2842105263 + 0.3473684211x + 0.2842105263 + x2 = 0 + 0.2842105263 Reorder the terms: -0.2842105263 + 0.2842105263 + 0.3473684211x + x2 = 0 + 0.2842105263 Combine like terms: -0.2842105263 + 0.2842105263 = 0.0000000000 0.0000000000 + 0.3473684211x + x2 = 0 + 0.2842105263 0.3473684211x + x2 = 0 + 0.2842105263 Combine like terms: 0 + 0.2842105263 = 0.2842105263 0.3473684211x + x2 = 0.2842105263 The x term is 0.3473684211x. Take half its coefficient (0.1736842106). Square it (0.03016620501) and add it to both sides. Add '0.03016620501' to each side of the equation. 0.3473684211x + 0.03016620501 + x2 = 0.2842105263 + 0.03016620501 Reorder the terms: 0.03016620501 + 0.3473684211x + x2 = 0.2842105263 + 0.03016620501 Combine like terms: 0.2842105263 + 0.03016620501 = 0.31437673131 0.03016620501 + 0.3473684211x + x2 = 0.31437673131 Factor a perfect square on the left side: (x + 0.1736842106)(x + 0.1736842106) = 0.31437673131 Calculate the square root of the right side: 0.560693081 Break this problem into two subproblems by setting (x + 0.1736842106) equal to 0.560693081 and -0.560693081.Subproblem 1
x + 0.1736842106 = 0.560693081 Simplifying x + 0.1736842106 = 0.560693081 Reorder the terms: 0.1736842106 + x = 0.560693081 Solving 0.1736842106 + x = 0.560693081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1736842106' to each side of the equation. 0.1736842106 + -0.1736842106 + x = 0.560693081 + -0.1736842106 Combine like terms: 0.1736842106 + -0.1736842106 = 0.0000000000 0.0000000000 + x = 0.560693081 + -0.1736842106 x = 0.560693081 + -0.1736842106 Combine like terms: 0.560693081 + -0.1736842106 = 0.3870088704 x = 0.3870088704 Simplifying x = 0.3870088704Subproblem 2
x + 0.1736842106 = -0.560693081 Simplifying x + 0.1736842106 = -0.560693081 Reorder the terms: 0.1736842106 + x = -0.560693081 Solving 0.1736842106 + x = -0.560693081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1736842106' to each side of the equation. 0.1736842106 + -0.1736842106 + x = -0.560693081 + -0.1736842106 Combine like terms: 0.1736842106 + -0.1736842106 = 0.0000000000 0.0000000000 + x = -0.560693081 + -0.1736842106 x = -0.560693081 + -0.1736842106 Combine like terms: -0.560693081 + -0.1736842106 = -0.7343772916 x = -0.7343772916 Simplifying x = -0.7343772916Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3870088704, -0.7343772916}
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