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Simplifying 0 = x2 + 80x + 11600 Reorder the terms: 0 = 11600 + 80x + x2 Solving 0 = 11600 + 80x + x2 Solving for variable 'x'. Combine like terms: 0 + -11600 = -11600 -11600 + -80x + -1x2 = 11600 + 80x + x2 + -11600 + -80x + -1x2 Reorder the terms: -11600 + -80x + -1x2 = 11600 + -11600 + 80x + -80x + x2 + -1x2 Combine like terms: 11600 + -11600 = 0 -11600 + -80x + -1x2 = 0 + 80x + -80x + x2 + -1x2 -11600 + -80x + -1x2 = 80x + -80x + x2 + -1x2 Combine like terms: 80x + -80x = 0 -11600 + -80x + -1x2 = 0 + x2 + -1x2 -11600 + -80x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -11600 + -80x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(11600 + 80x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11600 + 80x + x2)' equal to zero and attempt to solve: Simplifying 11600 + 80x + x2 = 0 Solving 11600 + 80x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-11600' to each side of the equation. 11600 + 80x + -11600 + x2 = 0 + -11600 Reorder the terms: 11600 + -11600 + 80x + x2 = 0 + -11600 Combine like terms: 11600 + -11600 = 0 0 + 80x + x2 = 0 + -11600 80x + x2 = 0 + -11600 Combine like terms: 0 + -11600 = -11600 80x + x2 = -11600 The x term is 80x. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80x + 1600 + x2 = -11600 + 1600 Reorder the terms: 1600 + 80x + x2 = -11600 + 1600 Combine like terms: -11600 + 1600 = -10000 1600 + 80x + x2 = -10000 Factor a perfect square on the left side: (x + 40)(x + 40) = -10000 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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