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Simplifying 12x + -3x2 + 42 = 0 Reorder the terms: 42 + 12x + -3x2 = 0 Solving 42 + 12x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(14 + 4x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(14 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying 14 + 4x + -1x2 = 0 Solving 14 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14 + -4x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -4x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -4x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -4x + x2 = 0 + 14 -4x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -4x + x2 = 14 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 = 14 + 4 Reorder the terms: 4 + -4x + x2 = 14 + 4 Combine like terms: 14 + 4 = 18 4 + -4x + x2 = 18 Factor a perfect square on the left side: (x + -2)(x + -2) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + -2) equal to 4.242640687 and -4.242640687.Subproblem 1
x + -2 = 4.242640687 Simplifying x + -2 = 4.242640687 Reorder the terms: -2 + x = 4.242640687 Solving -2 + x = 4.242640687 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 = 4.242640687 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.242640687 + 2 x = 4.242640687 + 2 Combine like terms: 4.242640687 + 2 = 6.242640687 x = 6.242640687 Simplifying x = 6.242640687Subproblem 2
x + -2 = -4.242640687 Simplifying x + -2 = -4.242640687 Reorder the terms: -2 + x = -4.242640687 Solving -2 + x = -4.242640687 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 = -4.242640687 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.242640687 + 2 x = -4.242640687 + 2 Combine like terms: -4.242640687 + 2 = -2.242640687 x = -2.242640687 Simplifying x = -2.242640687Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.242640687, -2.242640687}Solution
x = {6.242640687, -2.242640687}
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