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Simplifying x2 + -9 = 49x2 + -126x + 81 Reorder the terms: -9 + x2 = 49x2 + -126x + 81 Reorder the terms: -9 + x2 = 81 + -126x + 49x2 Solving -9 + x2 = 81 + -126x + 49x2 Solving for variable 'x'. Reorder the terms: -9 + -81 + 126x + x2 + -49x2 = 81 + -126x + 49x2 + -81 + 126x + -49x2 Combine like terms: -9 + -81 = -90 -90 + 126x + x2 + -49x2 = 81 + -126x + 49x2 + -81 + 126x + -49x2 Combine like terms: x2 + -49x2 = -48x2 -90 + 126x + -48x2 = 81 + -126x + 49x2 + -81 + 126x + -49x2 Reorder the terms: -90 + 126x + -48x2 = 81 + -81 + -126x + 126x + 49x2 + -49x2 Combine like terms: 81 + -81 = 0 -90 + 126x + -48x2 = 0 + -126x + 126x + 49x2 + -49x2 -90 + 126x + -48x2 = -126x + 126x + 49x2 + -49x2 Combine like terms: -126x + 126x = 0 -90 + 126x + -48x2 = 0 + 49x2 + -49x2 -90 + 126x + -48x2 = 49x2 + -49x2 Combine like terms: 49x2 + -49x2 = 0 -90 + 126x + -48x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-15 + 21x + -8x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-15 + 21x + -8x2)' equal to zero and attempt to solve: Simplifying -15 + 21x + -8x2 = 0 Solving -15 + 21x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 1.875 + -2.625x + x2 = 0 Move the constant term to the right: Add '-1.875' to each side of the equation. 1.875 + -2.625x + -1.875 + x2 = 0 + -1.875 Reorder the terms: 1.875 + -1.875 + -2.625x + x2 = 0 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + -2.625x + x2 = 0 + -1.875 -2.625x + x2 = 0 + -1.875 Combine like terms: 0 + -1.875 = -1.875 -2.625x + x2 = -1.875 The x term is -2.625x. Take half its coefficient (-1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. -2.625x + 1.72265625 + x2 = -1.875 + 1.72265625 Reorder the terms: 1.72265625 + -2.625x + x2 = -1.875 + 1.72265625 Combine like terms: -1.875 + 1.72265625 = -0.15234375 1.72265625 + -2.625x + x2 = -0.15234375 Factor a perfect square on the left side: (x + -1.3125)(x + -1.3125) = -0.15234375 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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