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Simplifying -100 = 11x2 + 13x + -28 Reorder the terms: -100 = -28 + 13x + 11x2 Solving -100 = -28 + 13x + 11x2 Solving for variable 'x'. Combine like terms: -100 + 28 = -72 -72 + -13x + -11x2 = -28 + 13x + 11x2 + 28 + -13x + -11x2 Reorder the terms: -72 + -13x + -11x2 = -28 + 28 + 13x + -13x + 11x2 + -11x2 Combine like terms: -28 + 28 = 0 -72 + -13x + -11x2 = 0 + 13x + -13x + 11x2 + -11x2 -72 + -13x + -11x2 = 13x + -13x + 11x2 + -11x2 Combine like terms: 13x + -13x = 0 -72 + -13x + -11x2 = 0 + 11x2 + -11x2 -72 + -13x + -11x2 = 11x2 + -11x2 Combine like terms: 11x2 + -11x2 = 0 -72 + -13x + -11x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(72 + 13x + 11x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(72 + 13x + 11x2)' equal to zero and attempt to solve: Simplifying 72 + 13x + 11x2 = 0 Solving 72 + 13x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 6.545454545 + 1.181818182x + x2 = 0 Move the constant term to the right: Add '-6.545454545' to each side of the equation. 6.545454545 + 1.181818182x + -6.545454545 + x2 = 0 + -6.545454545 Reorder the terms: 6.545454545 + -6.545454545 + 1.181818182x + x2 = 0 + -6.545454545 Combine like terms: 6.545454545 + -6.545454545 = 0.000000000 0.000000000 + 1.181818182x + x2 = 0 + -6.545454545 1.181818182x + x2 = 0 + -6.545454545 Combine like terms: 0 + -6.545454545 = -6.545454545 1.181818182x + x2 = -6.545454545 The x term is 1.181818182x. Take half its coefficient (0.590909091). Square it (0.3491735538) and add it to both sides. Add '0.3491735538' to each side of the equation. 1.181818182x + 0.3491735538 + x2 = -6.545454545 + 0.3491735538 Reorder the terms: 0.3491735538 + 1.181818182x + x2 = -6.545454545 + 0.3491735538 Combine like terms: -6.545454545 + 0.3491735538 = -6.1962809912 0.3491735538 + 1.181818182x + x2 = -6.1962809912 Factor a perfect square on the left side: (x + 0.590909091)(x + 0.590909091) = -6.1962809912 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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