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Simplifying 3.3x2 + 1.9x + -2.4 = 0 Reorder the terms: -2.4 + 1.9x + 3.3x2 = 0 Solving -2.4 + 1.9x + 3.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.3 the coefficient of the squared term: Divide each side by '3.3'. -0.7272727273 + 0.5757575758x + x2 = 0 Move the constant term to the right: Add '0.7272727273' to each side of the equation. -0.7272727273 + 0.5757575758x + 0.7272727273 + x2 = 0 + 0.7272727273 Reorder the terms: -0.7272727273 + 0.7272727273 + 0.5757575758x + x2 = 0 + 0.7272727273 Combine like terms: -0.7272727273 + 0.7272727273 = 0.0000000000 0.0000000000 + 0.5757575758x + x2 = 0 + 0.7272727273 0.5757575758x + x2 = 0 + 0.7272727273 Combine like terms: 0 + 0.7272727273 = 0.7272727273 0.5757575758x + x2 = 0.7272727273 The x term is 0.5757575758x. Take half its coefficient (0.2878787879). Square it (0.08287419652) and add it to both sides. Add '0.08287419652' to each side of the equation. 0.5757575758x + 0.08287419652 + x2 = 0.7272727273 + 0.08287419652 Reorder the terms: 0.08287419652 + 0.5757575758x + x2 = 0.7272727273 + 0.08287419652 Combine like terms: 0.7272727273 + 0.08287419652 = 0.81014692382 0.08287419652 + 0.5757575758x + x2 = 0.81014692382 Factor a perfect square on the left side: (x + 0.2878787879)(x + 0.2878787879) = 0.81014692382 Calculate the square root of the right side: 0.900081621 Break this problem into two subproblems by setting (x + 0.2878787879) equal to 0.900081621 and -0.900081621.Subproblem 1
x + 0.2878787879 = 0.900081621 Simplifying x + 0.2878787879 = 0.900081621 Reorder the terms: 0.2878787879 + x = 0.900081621 Solving 0.2878787879 + x = 0.900081621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2878787879' to each side of the equation. 0.2878787879 + -0.2878787879 + x = 0.900081621 + -0.2878787879 Combine like terms: 0.2878787879 + -0.2878787879 = 0.0000000000 0.0000000000 + x = 0.900081621 + -0.2878787879 x = 0.900081621 + -0.2878787879 Combine like terms: 0.900081621 + -0.2878787879 = 0.6122028331 x = 0.6122028331 Simplifying x = 0.6122028331Subproblem 2
x + 0.2878787879 = -0.900081621 Simplifying x + 0.2878787879 = -0.900081621 Reorder the terms: 0.2878787879 + x = -0.900081621 Solving 0.2878787879 + x = -0.900081621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2878787879' to each side of the equation. 0.2878787879 + -0.2878787879 + x = -0.900081621 + -0.2878787879 Combine like terms: 0.2878787879 + -0.2878787879 = 0.0000000000 0.0000000000 + x = -0.900081621 + -0.2878787879 x = -0.900081621 + -0.2878787879 Combine like terms: -0.900081621 + -0.2878787879 = -1.1879604089 x = -1.1879604089 Simplifying x = -1.1879604089Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6122028331, -1.1879604089}
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