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Simplifying 2x2 + 4x + -192 = 0 Reorder the terms: -192 + 4x + 2x2 = 0 Solving -192 + 4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-96 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-96 + 2x + x2)' equal to zero and attempt to solve: Simplifying -96 + 2x + x2 = 0 Solving -96 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + 2x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + 2x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 2x + x2 = 0 + 96 2x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 2x + x2 = 96 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 96 + 1 Reorder the terms: 1 + 2x + x2 = 96 + 1 Combine like terms: 96 + 1 = 97 1 + 2x + x2 = 97 Factor a perfect square on the left side: (x + 1)(x + 1) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (x + 1) equal to 9.848857802 and -9.848857802.Subproblem 1
x + 1 = 9.848857802 Simplifying x + 1 = 9.848857802 Reorder the terms: 1 + x = 9.848857802 Solving 1 + x = 9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 9.848857802 + -1 Combine like terms: 1 + -1 = 0 0 + x = 9.848857802 + -1 x = 9.848857802 + -1 Combine like terms: 9.848857802 + -1 = 8.848857802 x = 8.848857802 Simplifying x = 8.848857802Subproblem 2
x + 1 = -9.848857802 Simplifying x + 1 = -9.848857802 Reorder the terms: 1 + x = -9.848857802 Solving 1 + x = -9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -9.848857802 + -1 Combine like terms: 1 + -1 = 0 0 + x = -9.848857802 + -1 x = -9.848857802 + -1 Combine like terms: -9.848857802 + -1 = -10.848857802 x = -10.848857802 Simplifying x = -10.848857802Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.848857802, -10.848857802}Solution
x = {8.848857802, -10.848857802}
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