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Simplifying 0 = 9(x2 + 6x) + -18 Reorder the terms: 0 = 9(6x + x2) + -18 0 = (6x * 9 + x2 * 9) + -18 0 = (54x + 9x2) + -18 Reorder the terms: 0 = -18 + 54x + 9x2 Solving 0 = -18 + 54x + 9x2 Solving for variable 'x'. Combine like terms: 0 + 18 = 18 18 + -54x + -9x2 = -18 + 54x + 9x2 + 18 + -54x + -9x2 Reorder the terms: 18 + -54x + -9x2 = -18 + 18 + 54x + -54x + 9x2 + -9x2 Combine like terms: -18 + 18 = 0 18 + -54x + -9x2 = 0 + 54x + -54x + 9x2 + -9x2 18 + -54x + -9x2 = 54x + -54x + 9x2 + -9x2 Combine like terms: 54x + -54x = 0 18 + -54x + -9x2 = 0 + 9x2 + -9x2 18 + -54x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 18 + -54x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(2 + -6x + -1x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(2 + -6x + -1x2)' equal to zero and attempt to solve: Simplifying 2 + -6x + -1x2 = 0 Solving 2 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + 6x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 6x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 6x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 6x + x2 = 0 + 2 6x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 6x + x2 = 2 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 2 + 9 Reorder the terms: 9 + 6x + x2 = 2 + 9 Combine like terms: 2 + 9 = 11 9 + 6x + x2 = 11 Factor a perfect square on the left side: (x + 3)(x + 3) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + 3) equal to 3.31662479 and -3.31662479.Subproblem 1
x + 3 = 3.31662479 Simplifying x + 3 = 3.31662479 Reorder the terms: 3 + x = 3.31662479 Solving 3 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.31662479 + -3 x = 3.31662479 + -3 Combine like terms: 3.31662479 + -3 = 0.31662479 x = 0.31662479 Simplifying x = 0.31662479Subproblem 2
x + 3 = -3.31662479 Simplifying x + 3 = -3.31662479 Reorder the terms: 3 + x = -3.31662479 Solving 3 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.31662479 + -3 x = -3.31662479 + -3 Combine like terms: -3.31662479 + -3 = -6.31662479 x = -6.31662479 Simplifying x = -6.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.31662479, -6.31662479}Solution
x = {0.31662479, -6.31662479}
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