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Simplifying 3(7x + -5) = 5x(8x + 6) Reorder the terms: 3(-5 + 7x) = 5x(8x + 6) (-5 * 3 + 7x * 3) = 5x(8x + 6) (-15 + 21x) = 5x(8x + 6) Reorder the terms: -15 + 21x = 5x(6 + 8x) -15 + 21x = (6 * 5x + 8x * 5x) -15 + 21x = (30x + 40x2) Solving -15 + 21x = 30x + 40x2 Solving for variable 'x'. Combine like terms: 21x + -30x = -9x -15 + -9x + -40x2 = 30x + 40x2 + -30x + -40x2 Reorder the terms: -15 + -9x + -40x2 = 30x + -30x + 40x2 + -40x2 Combine like terms: 30x + -30x = 0 -15 + -9x + -40x2 = 0 + 40x2 + -40x2 -15 + -9x + -40x2 = 40x2 + -40x2 Combine like terms: 40x2 + -40x2 = 0 -15 + -9x + -40x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 9x + 40x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 9x + 40x2)' equal to zero and attempt to solve: Simplifying 15 + 9x + 40x2 = 0 Solving 15 + 9x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. 0.375 + 0.225x + x2 = 0.0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 0.225x + -0.375 + x2 = 0.0 + -0.375 Reorder the terms: 0.375 + -0.375 + 0.225x + x2 = 0.0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 0.225x + x2 = 0.0 + -0.375 0.225x + x2 = 0.0 + -0.375 Combine like terms: 0.0 + -0.375 = -0.375 0.225x + x2 = -0.375 The x term is 0.225x. Take half its coefficient (0.1125). Square it (0.01265625) and add it to both sides. Add '0.01265625' to each side of the equation. 0.225x + 0.01265625 + x2 = -0.375 + 0.01265625 Reorder the terms: 0.01265625 + 0.225x + x2 = -0.375 + 0.01265625 Combine like terms: -0.375 + 0.01265625 = -0.36234375 0.01265625 + 0.225x + x2 = -0.36234375 Factor a perfect square on the left side: (x + 0.1125)(x + 0.1125) = -0.36234375 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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