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Simplifying 10x2 + 55x + 105 = 0 Reorder the terms: 105 + 55x + 10x2 = 0 Solving 105 + 55x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(21 + 11x + 2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(21 + 11x + 2x2)' equal to zero and attempt to solve: Simplifying 21 + 11x + 2x2 = 0 Solving 21 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10.5 + 5.5x + x2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + 5.5x + -10.5 + x2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + 5.5x + x2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + 5.5x + x2 = 0 + -10.5 5.5x + x2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 5.5x + x2 = -10.5 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = -10.5 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = -10.5 + 7.5625 Combine like terms: -10.5 + 7.5625 = -2.9375 7.5625 + 5.5x + x2 = -2.9375 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = -2.9375 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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