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Simplifying (6x + 3)(x + -9) = 9 Reorder the terms: (3 + 6x)(x + -9) = 9 Reorder the terms: (3 + 6x)(-9 + x) = 9 Multiply (3 + 6x) * (-9 + x) (3(-9 + x) + 6x * (-9 + x)) = 9 ((-9 * 3 + x * 3) + 6x * (-9 + x)) = 9 ((-27 + 3x) + 6x * (-9 + x)) = 9 (-27 + 3x + (-9 * 6x + x * 6x)) = 9 (-27 + 3x + (-54x + 6x2)) = 9 Combine like terms: 3x + -54x = -51x (-27 + -51x + 6x2) = 9 Solving -27 + -51x + 6x2 = 9 Solving for variable 'x'. Reorder the terms: -27 + -9 + -51x + 6x2 = 9 + -9 Combine like terms: -27 + -9 = -36 -36 + -51x + 6x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -36 + -51x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-12 + -17x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-12 + -17x + 2x2)' equal to zero and attempt to solve: Simplifying -12 + -17x + 2x2 = 0 Solving -12 + -17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + -8.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -8.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -8.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -8.5x + x2 = 0 + 6 -8.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -8.5x + x2 = 6 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = 6 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = 6 + 18.0625 Combine like terms: 6 + 18.0625 = 24.0625 18.0625 + -8.5x + x2 = 24.0625 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 24.0625 Calculate the square root of the right side: 4.905354218 Break this problem into two subproblems by setting (x + -4.25) equal to 4.905354218 and -4.905354218.Subproblem 1
x + -4.25 = 4.905354218 Simplifying x + -4.25 = 4.905354218 Reorder the terms: -4.25 + x = 4.905354218 Solving -4.25 + x = 4.905354218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 4.905354218 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 4.905354218 + 4.25 x = 4.905354218 + 4.25 Combine like terms: 4.905354218 + 4.25 = 9.155354218 x = 9.155354218 Simplifying x = 9.155354218Subproblem 2
x + -4.25 = -4.905354218 Simplifying x + -4.25 = -4.905354218 Reorder the terms: -4.25 + x = -4.905354218 Solving -4.25 + x = -4.905354218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -4.905354218 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -4.905354218 + 4.25 x = -4.905354218 + 4.25 Combine like terms: -4.905354218 + 4.25 = -0.655354218 x = -0.655354218 Simplifying x = -0.655354218Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.155354218, -0.655354218}Solution
x = {9.155354218, -0.655354218}
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