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Simplifying (x2 + 4x + -6) + (2x2 + x + -8) = 0 Reorder the terms: (-6 + 4x + x2) + (2x2 + x + -8) = 0 Remove parenthesis around (-6 + 4x + x2) -6 + 4x + x2 + (2x2 + x + -8) = 0 Reorder the terms: -6 + 4x + x2 + (-8 + x + 2x2) = 0 Remove parenthesis around (-8 + x + 2x2) -6 + 4x + x2 + -8 + x + 2x2 = 0 Reorder the terms: -6 + -8 + 4x + x + x2 + 2x2 = 0 Combine like terms: -6 + -8 = -14 -14 + 4x + x + x2 + 2x2 = 0 Combine like terms: 4x + x = 5x -14 + 5x + x2 + 2x2 = 0 Combine like terms: x2 + 2x2 = 3x2 -14 + 5x + 3x2 = 0 Solving -14 + 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'. -4.666666667 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '4.666666667' to each side of the equation. -4.666666667 + 1.666666667x + 4.666666667 + x2 = 0 + 4.666666667 Reorder the terms: -4.666666667 + 4.666666667 + 1.666666667x + x2 = 0 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + 4.666666667 1.666666667x + x2 = 0 + 4.666666667 Combine like terms: 0 + 4.666666667 = 4.666666667 1.666666667x + x2 = 4.666666667 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 = 4.666666667 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 4.666666667 + 0.6944444447 Combine like terms: 4.666666667 + 0.6944444447 = 5.3611111117 0.6944444447 + 1.666666667x + x2 = 5.3611111117 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 5.3611111117 Calculate the square root of the right side: 2.315407332 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 2.315407332 and -2.315407332.Subproblem 1
x + 0.8333333335 = 2.315407332 Simplifying x + 0.8333333335 = 2.315407332 Reorder the terms: 0.8333333335 + x = 2.315407332 Solving 0.8333333335 + x = 2.315407332 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 = 2.315407332 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 2.315407332 + -0.8333333335 x = 2.315407332 + -0.8333333335 Combine like terms: 2.315407332 + -0.8333333335 = 1.4820739985 x = 1.4820739985 Simplifying x = 1.4820739985Subproblem 2
x + 0.8333333335 = -2.315407332 Simplifying x + 0.8333333335 = -2.315407332 Reorder the terms: 0.8333333335 + x = -2.315407332 Solving 0.8333333335 + x = -2.315407332 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 = -2.315407332 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -2.315407332 + -0.8333333335 x = -2.315407332 + -0.8333333335 Combine like terms: -2.315407332 + -0.8333333335 = -3.1487406655 x = -3.1487406655 Simplifying x = -3.1487406655Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4820739985, -3.1487406655}
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