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Simplifying (3x + 3)(4x + -1) = 144 Reorder the terms: (3 + 3x)(4x + -1) = 144 Reorder the terms: (3 + 3x)(-1 + 4x) = 144 Multiply (3 + 3x) * (-1 + 4x) (3(-1 + 4x) + 3x * (-1 + 4x)) = 144 ((-1 * 3 + 4x * 3) + 3x * (-1 + 4x)) = 144 ((-3 + 12x) + 3x * (-1 + 4x)) = 144 (-3 + 12x + (-1 * 3x + 4x * 3x)) = 144 (-3 + 12x + (-3x + 12x2)) = 144 Combine like terms: 12x + -3x = 9x (-3 + 9x + 12x2) = 144 Solving -3 + 9x + 12x2 = 144 Solving for variable 'x'. Reorder the terms: -3 + -144 + 9x + 12x2 = 144 + -144 Combine like terms: -3 + -144 = -147 -147 + 9x + 12x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -147 + 9x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-49 + 3x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-49 + 3x + 4x2)' equal to zero and attempt to solve: Simplifying -49 + 3x + 4x2 = 0 Solving -49 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.25 + 0.75x + x2 = 0 Move the constant term to the right: Add '12.25' to each side of the equation. -12.25 + 0.75x + 12.25 + x2 = 0 + 12.25 Reorder the terms: -12.25 + 12.25 + 0.75x + x2 = 0 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + 0.75x + x2 = 0 + 12.25 0.75x + x2 = 0 + 12.25 Combine like terms: 0 + 12.25 = 12.25 0.75x + x2 = 12.25 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 12.25 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 12.25 + 0.140625 Combine like terms: 12.25 + 0.140625 = 12.390625 0.140625 + 0.75x + x2 = 12.390625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 12.390625 Calculate the square root of the right side: 3.52003196 Break this problem into two subproblems by setting (x + 0.375) equal to 3.52003196 and -3.52003196.Subproblem 1
x + 0.375 = 3.52003196 Simplifying x + 0.375 = 3.52003196 Reorder the terms: 0.375 + x = 3.52003196 Solving 0.375 + x = 3.52003196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 3.52003196 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 3.52003196 + -0.375 x = 3.52003196 + -0.375 Combine like terms: 3.52003196 + -0.375 = 3.14503196 x = 3.14503196 Simplifying x = 3.14503196Subproblem 2
x + 0.375 = -3.52003196 Simplifying x + 0.375 = -3.52003196 Reorder the terms: 0.375 + x = -3.52003196 Solving 0.375 + x = -3.52003196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -3.52003196 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -3.52003196 + -0.375 x = -3.52003196 + -0.375 Combine like terms: -3.52003196 + -0.375 = -3.89503196 x = -3.89503196 Simplifying x = -3.89503196Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.14503196, -3.89503196}Solution
x = {3.14503196, -3.89503196}
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