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Simplifying 10x2 + 20x + 92 = 6 Reorder the terms: 92 + 20x + 10x2 = 6 Solving 92 + 20x + 10x2 = 6 Solving for variable 'x'. Reorder the terms: 92 + -6 + 20x + 10x2 = 6 + -6 Combine like terms: 92 + -6 = 86 86 + 20x + 10x2 = 6 + -6 Combine like terms: 6 + -6 = 0 86 + 20x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(43 + 10x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(43 + 10x + 5x2)' equal to zero and attempt to solve: Simplifying 43 + 10x + 5x2 = 0 Solving 43 + 10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 8.6 + 2x + x2 = 0 Move the constant term to the right: Add '-8.6' to each side of the equation. 8.6 + 2x + -8.6 + x2 = 0 + -8.6 Reorder the terms: 8.6 + -8.6 + 2x + x2 = 0 + -8.6 Combine like terms: 8.6 + -8.6 = 0.0 0.0 + 2x + x2 = 0 + -8.6 2x + x2 = 0 + -8.6 Combine like terms: 0 + -8.6 = -8.6 2x + x2 = -8.6 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -8.6 + 1 Reorder the terms: 1 + 2x + x2 = -8.6 + 1 Combine like terms: -8.6 + 1 = -7.6 1 + 2x + x2 = -7.6 Factor a perfect square on the left side: (x + 1)(x + 1) = -7.6 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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