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Simplifying 0 = 9x2 + 52x + 100 Reorder the terms: 0 = 100 + 52x + 9x2 Solving 0 = 100 + 52x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -100 = -100 -100 + -52x + -9x2 = 100 + 52x + 9x2 + -100 + -52x + -9x2 Reorder the terms: -100 + -52x + -9x2 = 100 + -100 + 52x + -52x + 9x2 + -9x2 Combine like terms: 100 + -100 = 0 -100 + -52x + -9x2 = 0 + 52x + -52x + 9x2 + -9x2 -100 + -52x + -9x2 = 52x + -52x + 9x2 + -9x2 Combine like terms: 52x + -52x = 0 -100 + -52x + -9x2 = 0 + 9x2 + -9x2 -100 + -52x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -100 + -52x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(100 + 52x + 9x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(100 + 52x + 9x2)' equal to zero and attempt to solve: Simplifying 100 + 52x + 9x2 = 0 Solving 100 + 52x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 11.11111111 + 5.777777778x + x2 = 0 Move the constant term to the right: Add '-11.11111111' to each side of the equation. 11.11111111 + 5.777777778x + -11.11111111 + x2 = 0 + -11.11111111 Reorder the terms: 11.11111111 + -11.11111111 + 5.777777778x + x2 = 0 + -11.11111111 Combine like terms: 11.11111111 + -11.11111111 = 0.00000000 0.00000000 + 5.777777778x + x2 = 0 + -11.11111111 5.777777778x + x2 = 0 + -11.11111111 Combine like terms: 0 + -11.11111111 = -11.11111111 5.777777778x + x2 = -11.11111111 The x term is 5.777777778x. Take half its coefficient (2.888888889). Square it (8.345679013) and add it to both sides. Add '8.345679013' to each side of the equation. 5.777777778x + 8.345679013 + x2 = -11.11111111 + 8.345679013 Reorder the terms: 8.345679013 + 5.777777778x + x2 = -11.11111111 + 8.345679013 Combine like terms: -11.11111111 + 8.345679013 = -2.765432097 8.345679013 + 5.777777778x + x2 = -2.765432097 Factor a perfect square on the left side: (x + 2.888888889)(x + 2.888888889) = -2.765432097 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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