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Simplifying 24x2 + 9x + -35 = 0 Reorder the terms: -35 + 9x + 24x2 = 0 Solving -35 + 9x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -1.458333333 + 0.375x + x2 = 0 Move the constant term to the right: Add '1.458333333' to each side of the equation. -1.458333333 + 0.375x + 1.458333333 + x2 = 0 + 1.458333333 Reorder the terms: -1.458333333 + 1.458333333 + 0.375x + x2 = 0 + 1.458333333 Combine like terms: -1.458333333 + 1.458333333 = 0.000000000 0.000000000 + 0.375x + x2 = 0 + 1.458333333 0.375x + x2 = 0 + 1.458333333 Combine like terms: 0 + 1.458333333 = 1.458333333 0.375x + x2 = 1.458333333 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 1.458333333 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 1.458333333 + 0.03515625 Combine like terms: 1.458333333 + 0.03515625 = 1.493489583 0.03515625 + 0.375x + x2 = 1.493489583 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 1.493489583 Calculate the square root of the right side: 1.222084115 Break this problem into two subproblems by setting (x + 0.1875) equal to 1.222084115 and -1.222084115.Subproblem 1
x + 0.1875 = 1.222084115 Simplifying x + 0.1875 = 1.222084115 Reorder the terms: 0.1875 + x = 1.222084115 Solving 0.1875 + x = 1.222084115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 1.222084115 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 1.222084115 + -0.1875 x = 1.222084115 + -0.1875 Combine like terms: 1.222084115 + -0.1875 = 1.034584115 x = 1.034584115 Simplifying x = 1.034584115Subproblem 2
x + 0.1875 = -1.222084115 Simplifying x + 0.1875 = -1.222084115 Reorder the terms: 0.1875 + x = -1.222084115 Solving 0.1875 + x = -1.222084115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -1.222084115 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -1.222084115 + -0.1875 x = -1.222084115 + -0.1875 Combine like terms: -1.222084115 + -0.1875 = -1.409584115 x = -1.409584115 Simplifying x = -1.409584115Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.034584115, -1.409584115}
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