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Simplifying (3x + -4)(3x + -8) = 35 Reorder the terms: (-4 + 3x)(3x + -8) = 35 Reorder the terms: (-4 + 3x)(-8 + 3x) = 35 Multiply (-4 + 3x) * (-8 + 3x) (-4(-8 + 3x) + 3x * (-8 + 3x)) = 35 ((-8 * -4 + 3x * -4) + 3x * (-8 + 3x)) = 35 ((32 + -12x) + 3x * (-8 + 3x)) = 35 (32 + -12x + (-8 * 3x + 3x * 3x)) = 35 (32 + -12x + (-24x + 9x2)) = 35 Combine like terms: -12x + -24x = -36x (32 + -36x + 9x2) = 35 Solving 32 + -36x + 9x2 = 35 Solving for variable 'x'. Reorder the terms: 32 + -35 + -36x + 9x2 = 35 + -35 Combine like terms: 32 + -35 = -3 -3 + -36x + 9x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -3 + -36x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -12x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -12x + 3x2)' equal to zero and attempt to solve: Simplifying -1 + -12x + 3x2 = 0 Solving -1 + -12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + -4x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -4x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -4x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -4x + x2 = 0 + 0.3333333333 -4x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -4x + x2 = 0.3333333333 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 0.3333333333 + 4 Reorder the terms: 4 + -4x + x2 = 0.3333333333 + 4 Combine like terms: 0.3333333333 + 4 = 4.3333333333 4 + -4x + x2 = 4.3333333333 Factor a perfect square on the left side: (x + -2)(x + -2) = 4.3333333333 Calculate the square root of the right side: 2.081665999 Break this problem into two subproblems by setting (x + -2) equal to 2.081665999 and -2.081665999.Subproblem 1
x + -2 = 2.081665999 Simplifying x + -2 = 2.081665999 Reorder the terms: -2 + x = 2.081665999 Solving -2 + x = 2.081665999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.081665999 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.081665999 + 2 x = 2.081665999 + 2 Combine like terms: 2.081665999 + 2 = 4.081665999 x = 4.081665999 Simplifying x = 4.081665999Subproblem 2
x + -2 = -2.081665999 Simplifying x + -2 = -2.081665999 Reorder the terms: -2 + x = -2.081665999 Solving -2 + x = -2.081665999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.081665999 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.081665999 + 2 x = -2.081665999 + 2 Combine like terms: -2.081665999 + 2 = -0.081665999 x = -0.081665999 Simplifying x = -0.081665999Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.081665999, -0.081665999}Solution
x = {4.081665999, -0.081665999}
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