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Simplifying 0 = x2 + 82x + 2320 Reorder the terms: 0 = 2320 + 82x + x2 Solving 0 = 2320 + 82x + x2 Solving for variable 'x'. Combine like terms: 0 + -2320 = -2320 -2320 + -82x + -1x2 = 2320 + 82x + x2 + -2320 + -82x + -1x2 Reorder the terms: -2320 + -82x + -1x2 = 2320 + -2320 + 82x + -82x + x2 + -1x2 Combine like terms: 2320 + -2320 = 0 -2320 + -82x + -1x2 = 0 + 82x + -82x + x2 + -1x2 -2320 + -82x + -1x2 = 82x + -82x + x2 + -1x2 Combine like terms: 82x + -82x = 0 -2320 + -82x + -1x2 = 0 + x2 + -1x2 -2320 + -82x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -2320 + -82x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2320 + 82x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2320 + 82x + x2)' equal to zero and attempt to solve: Simplifying 2320 + 82x + x2 = 0 Solving 2320 + 82x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2320' to each side of the equation. 2320 + 82x + -2320 + x2 = 0 + -2320 Reorder the terms: 2320 + -2320 + 82x + x2 = 0 + -2320 Combine like terms: 2320 + -2320 = 0 0 + 82x + x2 = 0 + -2320 82x + x2 = 0 + -2320 Combine like terms: 0 + -2320 = -2320 82x + x2 = -2320 The x term is 82x. Take half its coefficient (41). Square it (1681) and add it to both sides. Add '1681' to each side of the equation. 82x + 1681 + x2 = -2320 + 1681 Reorder the terms: 1681 + 82x + x2 = -2320 + 1681 Combine like terms: -2320 + 1681 = -639 1681 + 82x + x2 = -639 Factor a perfect square on the left side: (x + 41)(x + 41) = -639 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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