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Simplifying 6x2 + 24x + -84 = 0 Reorder the terms: -84 + 24x + 6x2 = 0 Solving -84 + 24x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-14 + 4x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-14 + 4x + x2)' equal to zero and attempt to solve: Simplifying -14 + 4x + x2 = 0 Solving -14 + 4x + x2 = 0 Begin completing the square. 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 = 2.242640687 x = 2.242640687 Simplifying x = 2.242640687Subproblem 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 = -6.242640687 x = -6.242640687 Simplifying x = -6.242640687Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.242640687, -6.242640687}Solution
x = {2.242640687, -6.242640687}
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