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Simplifying 2x2 + 12x + -84 = 0 Reorder the terms: -84 + 12x + 2x2 = 0 Solving -84 + 12x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-42 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-42 + 6x + x2)' equal to zero and attempt to solve: Simplifying -42 + 6x + x2 = 0 Solving -42 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 6x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + 6x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 6x + x2 = 0 + 42 6x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 6x + x2 = 42 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 42 + 9 Reorder the terms: 9 + 6x + x2 = 42 + 9 Combine like terms: 42 + 9 = 51 9 + 6x + x2 = 51 Factor a perfect square on the left side: (x + 3)(x + 3) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (x + 3) equal to 7.141428429 and -7.141428429.Subproblem 1
x + 3 = 7.141428429 Simplifying x + 3 = 7.141428429 Reorder the terms: 3 + x = 7.141428429 Solving 3 + x = 7.141428429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 7.141428429 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.141428429 + -3 x = 7.141428429 + -3 Combine like terms: 7.141428429 + -3 = 4.141428429 x = 4.141428429 Simplifying x = 4.141428429Subproblem 2
x + 3 = -7.141428429 Simplifying x + 3 = -7.141428429 Reorder the terms: 3 + x = -7.141428429 Solving 3 + x = -7.141428429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -7.141428429 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.141428429 + -3 x = -7.141428429 + -3 Combine like terms: -7.141428429 + -3 = -10.141428429 x = -10.141428429 Simplifying x = -10.141428429Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.141428429, -10.141428429}Solution
x = {4.141428429, -10.141428429}
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