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Simplifying 3x2 + 5x + -330 = 0 Reorder the terms: -330 + 5x + 3x2 = 0 Solving -330 + 5x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -110 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '110' to each side of the equation. -110 + 1.666666667x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + 1.666666667x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 1.666666667x + x2 = 0 + 110 1.666666667x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 1.666666667x + x2 = 110 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 110 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 110 + 0.6944444447 Combine like terms: 110 + 0.6944444447 = 110.6944444447 0.6944444447 + 1.666666667x + x2 = 110.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 110.6944444447 Calculate the square root of the right side: 10.521142735 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 10.521142735 and -10.521142735.Subproblem 1
x + 0.8333333335 = 10.521142735 Simplifying x + 0.8333333335 = 10.521142735 Reorder the terms: 0.8333333335 + x = 10.521142735 Solving 0.8333333335 + x = 10.521142735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 10.521142735 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 10.521142735 + -0.8333333335 x = 10.521142735 + -0.8333333335 Combine like terms: 10.521142735 + -0.8333333335 = 9.6878094015 x = 9.6878094015 Simplifying x = 9.6878094015Subproblem 2
x + 0.8333333335 = -10.521142735 Simplifying x + 0.8333333335 = -10.521142735 Reorder the terms: 0.8333333335 + x = -10.521142735 Solving 0.8333333335 + x = -10.521142735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -10.521142735 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -10.521142735 + -0.8333333335 x = -10.521142735 + -0.8333333335 Combine like terms: -10.521142735 + -0.8333333335 = -11.3544760685 x = -11.3544760685 Simplifying x = -11.3544760685Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.6878094015, -11.3544760685}
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