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Simplifying x2 + -16x = -2x2 + -3x + -9 Reorder the terms: -16x + x2 = -2x2 + -3x + -9 Reorder the terms: -16x + x2 = -9 + -3x + -2x2 Solving -16x + x2 = -9 + -3x + -2x2 Solving for variable 'x'. Reorder the terms: 9 + -16x + 3x + x2 + 2x2 = -9 + -3x + -2x2 + 9 + 3x + 2x2 Combine like terms: -16x + 3x = -13x 9 + -13x + x2 + 2x2 = -9 + -3x + -2x2 + 9 + 3x + 2x2 Combine like terms: x2 + 2x2 = 3x2 9 + -13x + 3x2 = -9 + -3x + -2x2 + 9 + 3x + 2x2 Reorder the terms: 9 + -13x + 3x2 = -9 + 9 + -3x + 3x + -2x2 + 2x2 Combine like terms: -9 + 9 = 0 9 + -13x + 3x2 = 0 + -3x + 3x + -2x2 + 2x2 9 + -13x + 3x2 = -3x + 3x + -2x2 + 2x2 Combine like terms: -3x + 3x = 0 9 + -13x + 3x2 = 0 + -2x2 + 2x2 9 + -13x + 3x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 9 + -13x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3 + -4.333333333x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -4.333333333x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -4.333333333x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4.333333333x + x2 = 0 + -3 -4.333333333x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4.333333333x + x2 = -3 The x term is -4.333333333x. Take half its coefficient (-2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. -4.333333333x + 4.694444446 + x2 = -3 + 4.694444446 Reorder the terms: 4.694444446 + -4.333333333x + x2 = -3 + 4.694444446 Combine like terms: -3 + 4.694444446 = 1.694444446 4.694444446 + -4.333333333x + x2 = 1.694444446 Factor a perfect square on the left side: (x + -2.166666667)(x + -2.166666667) = 1.694444446 Calculate the square root of the right side: 1.30170828 Break this problem into two subproblems by setting (x + -2.166666667) equal to 1.30170828 and -1.30170828.Subproblem 1
x + -2.166666667 = 1.30170828 Simplifying x + -2.166666667 = 1.30170828 Reorder the terms: -2.166666667 + x = 1.30170828 Solving -2.166666667 + x = 1.30170828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = 1.30170828 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = 1.30170828 + 2.166666667 x = 1.30170828 + 2.166666667 Combine like terms: 1.30170828 + 2.166666667 = 3.468374947 x = 3.468374947 Simplifying x = 3.468374947Subproblem 2
x + -2.166666667 = -1.30170828 Simplifying x + -2.166666667 = -1.30170828 Reorder the terms: -2.166666667 + x = -1.30170828 Solving -2.166666667 + x = -1.30170828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = -1.30170828 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = -1.30170828 + 2.166666667 x = -1.30170828 + 2.166666667 Combine like terms: -1.30170828 + 2.166666667 = 0.864958387 x = 0.864958387 Simplifying x = 0.864958387Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.468374947, 0.864958387}
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