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Simplifying -9x(x + 6) = 3(x + 18) Reorder the terms: -9x(6 + x) = 3(x + 18) (6 * -9x + x * -9x) = 3(x + 18) (-54x + -9x2) = 3(x + 18) Reorder the terms: -54x + -9x2 = 3(18 + x) -54x + -9x2 = (18 * 3 + x * 3) -54x + -9x2 = (54 + 3x) Solving -54x + -9x2 = 54 + 3x Solving for variable 'x'. Reorder the terms: -54 + -54x + -3x + -9x2 = 54 + 3x + -54 + -3x Combine like terms: -54x + -3x = -57x -54 + -57x + -9x2 = 54 + 3x + -54 + -3x Reorder the terms: -54 + -57x + -9x2 = 54 + -54 + 3x + -3x Combine like terms: 54 + -54 = 0 -54 + -57x + -9x2 = 0 + 3x + -3x -54 + -57x + -9x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -54 + -57x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(18 + 19x + 3x2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(18 + 19x + 3x2)' equal to zero and attempt to solve: Simplifying 18 + 19x + 3x2 = 0 Solving 18 + 19x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 6 + 6.333333333x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 6.333333333x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 6.333333333x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 6.333333333x + x2 = 0 + -6 6.333333333x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 6.333333333x + x2 = -6 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 = -6 + 10.02777778 Reorder the terms: 10.02777778 + 6.333333333x + x2 = -6 + 10.02777778 Combine like terms: -6 + 10.02777778 = 4.02777778 10.02777778 + 6.333333333x + x2 = 4.02777778 Factor a perfect square on the left side: (x + 3.166666667)(x + 3.166666667) = 4.02777778 Calculate the square root of the right side: 2.00693243 Break this problem into two subproblems by setting (x + 3.166666667) equal to 2.00693243 and -2.00693243.Subproblem 1
x + 3.166666667 = 2.00693243 Simplifying x + 3.166666667 = 2.00693243 Reorder the terms: 3.166666667 + x = 2.00693243 Solving 3.166666667 + x = 2.00693243 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 = 2.00693243 + -3.166666667 Combine like terms: 3.166666667 + -3.166666667 = 0.000000000 0.000000000 + x = 2.00693243 + -3.166666667 x = 2.00693243 + -3.166666667 Combine like terms: 2.00693243 + -3.166666667 = -1.159734237 x = -1.159734237 Simplifying x = -1.159734237Subproblem 2
x + 3.166666667 = -2.00693243 Simplifying x + 3.166666667 = -2.00693243 Reorder the terms: 3.166666667 + x = -2.00693243 Solving 3.166666667 + x = -2.00693243 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 = -2.00693243 + -3.166666667 Combine like terms: 3.166666667 + -3.166666667 = 0.000000000 0.000000000 + x = -2.00693243 + -3.166666667 x = -2.00693243 + -3.166666667 Combine like terms: -2.00693243 + -3.166666667 = -5.173599097 x = -5.173599097 Simplifying x = -5.173599097Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.159734237, -5.173599097}Solution
x = {-1.159734237, -5.173599097}
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