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Simplifying (3x2 + -5x + -66) = 0 Reorder the terms: (-66 + -5x + 3x2) = 0 Remove parenthesis around (-66 + -5x + 3x2) -66 + -5x + 3x2 = 0 Solving -66 + -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'. -22 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + -1.666666667x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + -1.666666667x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -1.666666667x + x2 = 0 + 22 -1.666666667x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 -1.666666667x + x2 = 22 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 = 22 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 22 + 0.6944444447 Combine like terms: 22 + 0.6944444447 = 22.6944444447 0.6944444447 + -1.666666667x + x2 = 22.6944444447 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 22.6944444447 Calculate the square root of the right side: 4.763868643 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 4.763868643 and -4.763868643.Subproblem 1
x + -0.8333333335 = 4.763868643 Simplifying x + -0.8333333335 = 4.763868643 Reorder the terms: -0.8333333335 + x = 4.763868643 Solving -0.8333333335 + x = 4.763868643 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 = 4.763868643 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 4.763868643 + 0.8333333335 x = 4.763868643 + 0.8333333335 Combine like terms: 4.763868643 + 0.8333333335 = 5.5972019765 x = 5.5972019765 Simplifying x = 5.5972019765Subproblem 2
x + -0.8333333335 = -4.763868643 Simplifying x + -0.8333333335 = -4.763868643 Reorder the terms: -0.8333333335 + x = -4.763868643 Solving -0.8333333335 + x = -4.763868643 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 = -4.763868643 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -4.763868643 + 0.8333333335 x = -4.763868643 + 0.8333333335 Combine like terms: -4.763868643 + 0.8333333335 = -3.9305353095 x = -3.9305353095 Simplifying x = -3.9305353095Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.5972019765, -3.9305353095}
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