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Simplifying 2x2 + 8x + -84 = 0 Reorder the terms: -84 + 8x + 2x2 = 0 Solving -84 + 8x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-42 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-42 + 4x + x2)' equal to zero and attempt to solve: Simplifying -42 + 4x + x2 = 0 Solving -42 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 4x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + 4x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 4x + x2 = 0 + 42 4x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 4x + x2 = 42 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 = 42 + 4 Reorder the terms: 4 + 4x + x2 = 42 + 4 Combine like terms: 42 + 4 = 46 4 + 4x + x2 = 46 Factor a perfect square on the left side: (x + 2)(x + 2) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (x + 2) equal to 6.782329983 and -6.782329983.Subproblem 1
x + 2 = 6.782329983 Simplifying x + 2 = 6.782329983 Reorder the terms: 2 + x = 6.782329983 Solving 2 + x = 6.782329983 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 = 6.782329983 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.782329983 + -2 x = 6.782329983 + -2 Combine like terms: 6.782329983 + -2 = 4.782329983 x = 4.782329983 Simplifying x = 4.782329983Subproblem 2
x + 2 = -6.782329983 Simplifying x + 2 = -6.782329983 Reorder the terms: 2 + x = -6.782329983 Solving 2 + x = -6.782329983 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 = -6.782329983 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.782329983 + -2 x = -6.782329983 + -2 Combine like terms: -6.782329983 + -2 = -8.782329983 x = -8.782329983 Simplifying x = -8.782329983Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.782329983, -8.782329983}Solution
x = {4.782329983, -8.782329983}
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