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Simplifying 12(x + 3) = 4(2x + -9) * 4x Reorder the terms: 12(3 + x) = 4(2x + -9) * 4x (3 * 12 + x * 12) = 4(2x + -9) * 4x (36 + 12x) = 4(2x + -9) * 4x Reorder the terms: 36 + 12x = 4(-9 + 2x) * 4x Reorder the terms for easier multiplication: 36 + 12x = 4 * 4x(-9 + 2x) Multiply 4 * 4 36 + 12x = 16x(-9 + 2x) 36 + 12x = (-9 * 16x + 2x * 16x) 36 + 12x = (-144x + 32x2) Solving 36 + 12x = -144x + 32x2 Solving for variable 'x'. Combine like terms: 12x + 144x = 156x 36 + 156x + -32x2 = -144x + 32x2 + 144x + -32x2 Reorder the terms: 36 + 156x + -32x2 = -144x + 144x + 32x2 + -32x2 Combine like terms: -144x + 144x = 0 36 + 156x + -32x2 = 0 + 32x2 + -32x2 36 + 156x + -32x2 = 32x2 + -32x2 Combine like terms: 32x2 + -32x2 = 0 36 + 156x + -32x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(9 + 39x + -8x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(9 + 39x + -8x2)' equal to zero and attempt to solve: Simplifying 9 + 39x + -8x2 = 0 Solving 9 + 39x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.125 + -4.875x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -4.875x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -4.875x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -4.875x + x2 = 0 + 1.125 -4.875x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -4.875x + x2 = 1.125 The x term is -4.875x. Take half its coefficient (-2.4375). Square it (5.94140625) and add it to both sides. Add '5.94140625' to each side of the equation. -4.875x + 5.94140625 + x2 = 1.125 + 5.94140625 Reorder the terms: 5.94140625 + -4.875x + x2 = 1.125 + 5.94140625 Combine like terms: 1.125 + 5.94140625 = 7.06640625 5.94140625 + -4.875x + x2 = 7.06640625 Factor a perfect square on the left side: (x + -2.4375)(x + -2.4375) = 7.06640625 Calculate the square root of the right side: 2.65827129 Break this problem into two subproblems by setting (x + -2.4375) equal to 2.65827129 and -2.65827129.Subproblem 1
x + -2.4375 = 2.65827129 Simplifying x + -2.4375 = 2.65827129 Reorder the terms: -2.4375 + x = 2.65827129 Solving -2.4375 + x = 2.65827129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4375' to each side of the equation. -2.4375 + 2.4375 + x = 2.65827129 + 2.4375 Combine like terms: -2.4375 + 2.4375 = 0.0000 0.0000 + x = 2.65827129 + 2.4375 x = 2.65827129 + 2.4375 Combine like terms: 2.65827129 + 2.4375 = 5.09577129 x = 5.09577129 Simplifying x = 5.09577129Subproblem 2
x + -2.4375 = -2.65827129 Simplifying x + -2.4375 = -2.65827129 Reorder the terms: -2.4375 + x = -2.65827129 Solving -2.4375 + x = -2.65827129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4375' to each side of the equation. -2.4375 + 2.4375 + x = -2.65827129 + 2.4375 Combine like terms: -2.4375 + 2.4375 = 0.0000 0.0000 + x = -2.65827129 + 2.4375 x = -2.65827129 + 2.4375 Combine like terms: -2.65827129 + 2.4375 = -0.22077129 x = -0.22077129 Simplifying x = -0.22077129Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.09577129, -0.22077129}Solution
x = {5.09577129, -0.22077129}
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