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Simplifying 2x2 + 80x + -96 = 0 Reorder the terms: -96 + 80x + 2x2 = 0 Solving -96 + 80x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-48 + 40x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-48 + 40x + x2)' equal to zero and attempt to solve: Simplifying -48 + 40x + x2 = 0 Solving -48 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 40x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 40x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 40x + x2 = 0 + 48 40x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 40x + x2 = 48 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = 48 + 400 Reorder the terms: 400 + 40x + x2 = 48 + 400 Combine like terms: 48 + 400 = 448 400 + 40x + x2 = 448 Factor a perfect square on the left side: (x + 20)(x + 20) = 448 Calculate the square root of the right side: 21.166010489 Break this problem into two subproblems by setting (x + 20) equal to 21.166010489 and -21.166010489.Subproblem 1
x + 20 = 21.166010489 Simplifying x + 20 = 21.166010489 Reorder the terms: 20 + x = 21.166010489 Solving 20 + x = 21.166010489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 21.166010489 + -20 Combine like terms: 20 + -20 = 0 0 + x = 21.166010489 + -20 x = 21.166010489 + -20 Combine like terms: 21.166010489 + -20 = 1.166010489 x = 1.166010489 Simplifying x = 1.166010489Subproblem 2
x + 20 = -21.166010489 Simplifying x + 20 = -21.166010489 Reorder the terms: 20 + x = -21.166010489 Solving 20 + x = -21.166010489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -21.166010489 + -20 Combine like terms: 20 + -20 = 0 0 + x = -21.166010489 + -20 x = -21.166010489 + -20 Combine like terms: -21.166010489 + -20 = -41.166010489 x = -41.166010489 Simplifying x = -41.166010489Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.166010489, -41.166010489}Solution
x = {1.166010489, -41.166010489}
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