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Simplifying (4x2 + -8x + 9) + -1(x2 + 11x + -6) = 0 Reorder the terms: (9 + -8x + 4x2) + -1(x2 + 11x + -6) = 0 Remove parenthesis around (9 + -8x + 4x2) 9 + -8x + 4x2 + -1(x2 + 11x + -6) = 0 Reorder the terms: 9 + -8x + 4x2 + -1(-6 + 11x + x2) = 0 9 + -8x + 4x2 + (-6 * -1 + 11x * -1 + x2 * -1) = 0 9 + -8x + 4x2 + (6 + -11x + -1x2) = 0 Reorder the terms: 9 + 6 + -8x + -11x + 4x2 + -1x2 = 0 Combine like terms: 9 + 6 = 15 15 + -8x + -11x + 4x2 + -1x2 = 0 Combine like terms: -8x + -11x = -19x 15 + -19x + 4x2 + -1x2 = 0 Combine like terms: 4x2 + -1x2 = 3x2 15 + -19x + 3x2 = 0 Solving 15 + -19x + 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'. 5 + -6.333333333x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -6.333333333x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -6.333333333x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6.333333333x + x2 = 0 + -5 -6.333333333x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -6.333333333x + x2 = -5 The x term is -6.333333333x. Take half its coefficient (-3.166666667). Square it (10.02777778) and add it to both sides. Add '10.02777778' to each side of the equation. -6.333333333x + 10.02777778 + x2 = -5 + 10.02777778 Reorder the terms: 10.02777778 + -6.333333333x + x2 = -5 + 10.02777778 Combine like terms: -5 + 10.02777778 = 5.02777778 10.02777778 + -6.333333333x + x2 = 5.02777778 Factor a perfect square on the left side: (x + -3.166666667)(x + -3.166666667) = 5.02777778 Calculate the square root of the right side: 2.242270675 Break this problem into two subproblems by setting (x + -3.166666667) equal to 2.242270675 and -2.242270675.Subproblem 1
x + -3.166666667 = 2.242270675 Simplifying x + -3.166666667 = 2.242270675 Reorder the terms: -3.166666667 + x = 2.242270675 Solving -3.166666667 + x = 2.242270675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + x = 2.242270675 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = 2.242270675 + 3.166666667 x = 2.242270675 + 3.166666667 Combine like terms: 2.242270675 + 3.166666667 = 5.408937342 x = 5.408937342 Simplifying x = 5.408937342Subproblem 2
x + -3.166666667 = -2.242270675 Simplifying x + -3.166666667 = -2.242270675 Reorder the terms: -3.166666667 + x = -2.242270675 Solving -3.166666667 + x = -2.242270675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + x = -2.242270675 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = -2.242270675 + 3.166666667 x = -2.242270675 + 3.166666667 Combine like terms: -2.242270675 + 3.166666667 = 0.924395992 x = 0.924395992 Simplifying x = 0.924395992Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.408937342, 0.924395992}
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