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Simplifying 36 = 3x(x) + -3x + -2(x + -2) Multiply x * x 36 = 3x2 + -3x + -2(x + -2) Reorder the terms: 36 = 3x2 + -3x + -2(-2 + x) 36 = 3x2 + -3x + (-2 * -2 + x * -2) 36 = 3x2 + -3x + (4 + -2x) Reorder the terms: 36 = 4 + -3x + -2x + 3x2 Combine like terms: -3x + -2x = -5x 36 = 4 + -5x + 3x2 Solving 36 = 4 + -5x + 3x2 Solving for variable 'x'. Combine like terms: 36 + -4 = 32 32 + 5x + -3x2 = 4 + -5x + 3x2 + -4 + 5x + -3x2 Reorder the terms: 32 + 5x + -3x2 = 4 + -4 + -5x + 5x + 3x2 + -3x2 Combine like terms: 4 + -4 = 0 32 + 5x + -3x2 = 0 + -5x + 5x + 3x2 + -3x2 32 + 5x + -3x2 = -5x + 5x + 3x2 + -3x2 Combine like terms: -5x + 5x = 0 32 + 5x + -3x2 = 0 + 3x2 + -3x2 32 + 5x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 32 + 5x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -10.66666667 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '10.66666667' to each side of the equation. -10.66666667 + -1.666666667x + 10.66666667 + x2 = 0 + 10.66666667 Reorder the terms: -10.66666667 + 10.66666667 + -1.666666667x + x2 = 0 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + -1.666666667x + x2 = 0 + 10.66666667 -1.666666667x + x2 = 0 + 10.66666667 Combine like terms: 0 + 10.66666667 = 10.66666667 -1.666666667x + x2 = 10.66666667 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 = 10.66666667 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 10.66666667 + 0.6944444447 Combine like terms: 10.66666667 + 0.6944444447 = 11.3611111147 0.6944444447 + -1.666666667x + x2 = 11.3611111147 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 11.3611111147 Calculate the square root of the right side: 3.370624737 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 3.370624737 and -3.370624737.Subproblem 1
x + -0.8333333335 = 3.370624737 Simplifying x + -0.8333333335 = 3.370624737 Reorder the terms: -0.8333333335 + x = 3.370624737 Solving -0.8333333335 + x = 3.370624737 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 = 3.370624737 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 3.370624737 + 0.8333333335 x = 3.370624737 + 0.8333333335 Combine like terms: 3.370624737 + 0.8333333335 = 4.2039580705 x = 4.2039580705 Simplifying x = 4.2039580705Subproblem 2
x + -0.8333333335 = -3.370624737 Simplifying x + -0.8333333335 = -3.370624737 Reorder the terms: -0.8333333335 + x = -3.370624737 Solving -0.8333333335 + x = -3.370624737 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 = -3.370624737 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -3.370624737 + 0.8333333335 x = -3.370624737 + 0.8333333335 Combine like terms: -3.370624737 + 0.8333333335 = -2.5372914035 x = -2.5372914035 Simplifying x = -2.5372914035Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.2039580705, -2.5372914035}
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