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Simplifying 3x + -7 = 8x(x + 1) Reorder the terms: -7 + 3x = 8x(x + 1) Reorder the terms: -7 + 3x = 8x(1 + x) -7 + 3x = (1 * 8x + x * 8x) -7 + 3x = (8x + 8x2) Solving -7 + 3x = 8x + 8x2 Solving for variable 'x'. Combine like terms: 3x + -8x = -5x -7 + -5x + -8x2 = 8x + 8x2 + -8x + -8x2 Reorder the terms: -7 + -5x + -8x2 = 8x + -8x + 8x2 + -8x2 Combine like terms: 8x + -8x = 0 -7 + -5x + -8x2 = 0 + 8x2 + -8x2 -7 + -5x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -7 + -5x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 5x + 8x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 5x + 8x2)' equal to zero and attempt to solve: Simplifying 7 + 5x + 8x2 = 0 Solving 7 + 5x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.875 + 0.625x + x2 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + 0.625x + -0.875 + x2 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + 0.625x + x2 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + 0.625x + x2 = 0 + -0.875 0.625x + x2 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 0.625x + x2 = -0.875 The x term is 0.625x. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625x + 0.09765625 + x2 = -0.875 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x + x2 = -0.875 + 0.09765625 Combine like terms: -0.875 + 0.09765625 = -0.77734375 0.09765625 + 0.625x + x2 = -0.77734375 Factor a perfect square on the left side: (x + 0.3125)(x + 0.3125) = -0.77734375 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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