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Simplifying 3(x + 4) * 5x(11 + 3) = 12 Reorder the terms: 3(4 + x) * 5x(11 + 3) = 12 Combine like terms: 11 + 3 = 14 3(4 + x) * 5x(14) = 12 Reorder the terms for easier multiplication: 3 * 5 * 14x(4 + x) = 12 Multiply 3 * 5 15 * 14x(4 + x) = 12 Multiply 15 * 14 210x(4 + x) = 12 (4 * 210x + x * 210x) = 12 (840x + 210x2) = 12 Solving 840x + 210x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 840x + 210x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 840x + 210x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-2 + 140x + 35x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-2 + 140x + 35x2)' equal to zero and attempt to solve: Simplifying -2 + 140x + 35x2 = 0 Solving -2 + 140x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.05714285714 + 4x + x2 = 0 Move the constant term to the right: Add '0.05714285714' to each side of the equation. -0.05714285714 + 4x + 0.05714285714 + x2 = 0 + 0.05714285714 Reorder the terms: -0.05714285714 + 0.05714285714 + 4x + x2 = 0 + 0.05714285714 Combine like terms: -0.05714285714 + 0.05714285714 = 0.00000000000 0.00000000000 + 4x + x2 = 0 + 0.05714285714 4x + x2 = 0 + 0.05714285714 Combine like terms: 0 + 0.05714285714 = 0.05714285714 4x + x2 = 0.05714285714 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 = 0.05714285714 + 4 Reorder the terms: 4 + 4x + x2 = 0.05714285714 + 4 Combine like terms: 0.05714285714 + 4 = 4.05714285714 4 + 4x + x2 = 4.05714285714 Factor a perfect square on the left side: (x + 2)(x + 2) = 4.05714285714 Calculate the square root of the right side: 2.014235055 Break this problem into two subproblems by setting (x + 2) equal to 2.014235055 and -2.014235055.Subproblem 1
x + 2 = 2.014235055 Simplifying x + 2 = 2.014235055 Reorder the terms: 2 + x = 2.014235055 Solving 2 + x = 2.014235055 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 = 2.014235055 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.014235055 + -2 x = 2.014235055 + -2 Combine like terms: 2.014235055 + -2 = 0.014235055 x = 0.014235055 Simplifying x = 0.014235055Subproblem 2
x + 2 = -2.014235055 Simplifying x + 2 = -2.014235055 Reorder the terms: 2 + x = -2.014235055 Solving 2 + x = -2.014235055 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 = -2.014235055 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.014235055 + -2 x = -2.014235055 + -2 Combine like terms: -2.014235055 + -2 = -4.014235055 x = -4.014235055 Simplifying x = -4.014235055Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.014235055, -4.014235055}Solution
x = {0.014235055, -4.014235055}
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