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Simplifying 6x2 + 10x + -33 = 0 Reorder the terms: -33 + 10x + 6x2 = 0 Solving -33 + 10x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -5.5 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 1.666666667x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 1.666666667x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 1.666666667x + x2 = 0 + 5.5 1.666666667x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 1.666666667x + x2 = 5.5 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 = 5.5 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 5.5 + 0.6944444447 Combine like terms: 5.5 + 0.6944444447 = 6.1944444447 0.6944444447 + 1.666666667x + x2 = 6.1944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 6.1944444447 Calculate the square root of the right side: 2.488864087 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 2.488864087 and -2.488864087.Subproblem 1
x + 0.8333333335 = 2.488864087 Simplifying x + 0.8333333335 = 2.488864087 Reorder the terms: 0.8333333335 + x = 2.488864087 Solving 0.8333333335 + x = 2.488864087 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 = 2.488864087 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 2.488864087 + -0.8333333335 x = 2.488864087 + -0.8333333335 Combine like terms: 2.488864087 + -0.8333333335 = 1.6555307535 x = 1.6555307535 Simplifying x = 1.6555307535Subproblem 2
x + 0.8333333335 = -2.488864087 Simplifying x + 0.8333333335 = -2.488864087 Reorder the terms: 0.8333333335 + x = -2.488864087 Solving 0.8333333335 + x = -2.488864087 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 = -2.488864087 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -2.488864087 + -0.8333333335 x = -2.488864087 + -0.8333333335 Combine like terms: -2.488864087 + -0.8333333335 = -3.3221974205 x = -3.3221974205 Simplifying x = -3.3221974205Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6555307535, -3.3221974205}
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