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Simplifying 0 = x2 + 26x + 232 Reorder the terms: 0 = 232 + 26x + x2 Solving 0 = 232 + 26x + x2 Solving for variable 'x'. Combine like terms: 0 + -232 = -232 -232 + -26x + -1x2 = 232 + 26x + x2 + -232 + -26x + -1x2 Reorder the terms: -232 + -26x + -1x2 = 232 + -232 + 26x + -26x + x2 + -1x2 Combine like terms: 232 + -232 = 0 -232 + -26x + -1x2 = 0 + 26x + -26x + x2 + -1x2 -232 + -26x + -1x2 = 26x + -26x + x2 + -1x2 Combine like terms: 26x + -26x = 0 -232 + -26x + -1x2 = 0 + x2 + -1x2 -232 + -26x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -232 + -26x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(232 + 26x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(232 + 26x + x2)' equal to zero and attempt to solve: Simplifying 232 + 26x + x2 = 0 Solving 232 + 26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-232' to each side of the equation. 232 + 26x + -232 + x2 = 0 + -232 Reorder the terms: 232 + -232 + 26x + x2 = 0 + -232 Combine like terms: 232 + -232 = 0 0 + 26x + x2 = 0 + -232 26x + x2 = 0 + -232 Combine like terms: 0 + -232 = -232 26x + x2 = -232 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = -232 + 169 Reorder the terms: 169 + 26x + x2 = -232 + 169 Combine like terms: -232 + 169 = -63 169 + 26x + x2 = -63 Factor a perfect square on the left side: (x + 13)(x + 13) = -63 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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