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Simplifying 15x2 + -74x + -9 = 0 Reorder the terms: -9 + -74x + 15x2 = 0 Solving -9 + -74x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.6 + -4.933333333x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -4.933333333x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -4.933333333x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -4.933333333x + x2 = 0 + 0.6 -4.933333333x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -4.933333333x + x2 = 0.6 The x term is -4.933333333x. Take half its coefficient (-2.466666667). Square it (6.084444446) and add it to both sides. Add '6.084444446' to each side of the equation. -4.933333333x + 6.084444446 + x2 = 0.6 + 6.084444446 Reorder the terms: 6.084444446 + -4.933333333x + x2 = 0.6 + 6.084444446 Combine like terms: 0.6 + 6.084444446 = 6.684444446 6.084444446 + -4.933333333x + x2 = 6.684444446 Factor a perfect square on the left side: (x + -2.466666667)(x + -2.466666667) = 6.684444446 Calculate the square root of the right side: 2.585429258 Break this problem into two subproblems by setting (x + -2.466666667) equal to 2.585429258 and -2.585429258.Subproblem 1
x + -2.466666667 = 2.585429258 Simplifying x + -2.466666667 = 2.585429258 Reorder the terms: -2.466666667 + x = 2.585429258 Solving -2.466666667 + x = 2.585429258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.466666667' to each side of the equation. -2.466666667 + 2.466666667 + x = 2.585429258 + 2.466666667 Combine like terms: -2.466666667 + 2.466666667 = 0.000000000 0.000000000 + x = 2.585429258 + 2.466666667 x = 2.585429258 + 2.466666667 Combine like terms: 2.585429258 + 2.466666667 = 5.052095925 x = 5.052095925 Simplifying x = 5.052095925Subproblem 2
x + -2.466666667 = -2.585429258 Simplifying x + -2.466666667 = -2.585429258 Reorder the terms: -2.466666667 + x = -2.585429258 Solving -2.466666667 + x = -2.585429258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.466666667' to each side of the equation. -2.466666667 + 2.466666667 + x = -2.585429258 + 2.466666667 Combine like terms: -2.466666667 + 2.466666667 = 0.000000000 0.000000000 + x = -2.585429258 + 2.466666667 x = -2.585429258 + 2.466666667 Combine like terms: -2.585429258 + 2.466666667 = -0.118762591 x = -0.118762591 Simplifying x = -0.118762591Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.052095925, -0.118762591}
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