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Simplifying 10x2 + 4x + 77 = 9 Reorder the terms: 77 + 4x + 10x2 = 9 Solving 77 + 4x + 10x2 = 9 Solving for variable 'x'. Reorder the terms: 77 + -9 + 4x + 10x2 = 9 + -9 Combine like terms: 77 + -9 = 68 68 + 4x + 10x2 = 9 + -9 Combine like terms: 9 + -9 = 0 68 + 4x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(34 + 2x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(34 + 2x + 5x2)' equal to zero and attempt to solve: Simplifying 34 + 2x + 5x2 = 0 Solving 34 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 6.8 + 0.4x + x2 = 0 Move the constant term to the right: Add '-6.8' to each side of the equation. 6.8 + 0.4x + -6.8 + x2 = 0 + -6.8 Reorder the terms: 6.8 + -6.8 + 0.4x + x2 = 0 + -6.8 Combine like terms: 6.8 + -6.8 = 0.0 0.0 + 0.4x + x2 = 0 + -6.8 0.4x + x2 = 0 + -6.8 Combine like terms: 0 + -6.8 = -6.8 0.4x + x2 = -6.8 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = -6.8 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = -6.8 + 0.04 Combine like terms: -6.8 + 0.04 = -6.76 0.04 + 0.4x + x2 = -6.76 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = -6.76 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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