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Simplifying 2(6x2 + 2x) = 2(3x2 + 12) Reorder the terms: 2(2x + 6x2) = 2(3x2 + 12) (2x * 2 + 6x2 * 2) = 2(3x2 + 12) (4x + 12x2) = 2(3x2 + 12) Reorder the terms: 4x + 12x2 = 2(12 + 3x2) 4x + 12x2 = (12 * 2 + 3x2 * 2) 4x + 12x2 = (24 + 6x2) Solving 4x + 12x2 = 24 + 6x2 Solving for variable 'x'. Reorder the terms: -24 + 4x + 12x2 + -6x2 = 24 + 6x2 + -24 + -6x2 Combine like terms: 12x2 + -6x2 = 6x2 -24 + 4x + 6x2 = 24 + 6x2 + -24 + -6x2 Reorder the terms: -24 + 4x + 6x2 = 24 + -24 + 6x2 + -6x2 Combine like terms: 24 + -24 = 0 -24 + 4x + 6x2 = 0 + 6x2 + -6x2 -24 + 4x + 6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -24 + 4x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 2x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + 2x + 3x2)' equal to zero and attempt to solve: Simplifying -12 + 2x + 3x2 = 0 Solving -12 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.6666666667x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 0.6666666667x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.6666666667x + x2 = 0 + 4 0.6666666667x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.6666666667x + x2 = 4 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 4 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 4 + 0.1111111112 Combine like terms: 4 + 0.1111111112 = 4.1111111112 0.1111111112 + 0.6666666667x + x2 = 4.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 4.1111111112 Calculate the square root of the right side: 2.02758751 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 2.02758751 and -2.02758751.Subproblem 1
x + 0.3333333334 = 2.02758751 Simplifying x + 0.3333333334 = 2.02758751 Reorder the terms: 0.3333333334 + x = 2.02758751 Solving 0.3333333334 + x = 2.02758751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 2.02758751 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 2.02758751 + -0.3333333334 x = 2.02758751 + -0.3333333334 Combine like terms: 2.02758751 + -0.3333333334 = 1.6942541766 x = 1.6942541766 Simplifying x = 1.6942541766Subproblem 2
x + 0.3333333334 = -2.02758751 Simplifying x + 0.3333333334 = -2.02758751 Reorder the terms: 0.3333333334 + x = -2.02758751 Solving 0.3333333334 + x = -2.02758751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -2.02758751 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -2.02758751 + -0.3333333334 x = -2.02758751 + -0.3333333334 Combine like terms: -2.02758751 + -0.3333333334 = -2.3609208434 x = -2.3609208434 Simplifying x = -2.3609208434Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6942541766, -2.3609208434}Solution
x = {1.6942541766, -2.3609208434}
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