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Simplifying 6(5x + -8) + -20 = 11(2x + -3) * 3x Reorder the terms: 6(-8 + 5x) + -20 = 11(2x + -3) * 3x (-8 * 6 + 5x * 6) + -20 = 11(2x + -3) * 3x (-48 + 30x) + -20 = 11(2x + -3) * 3x Reorder the terms: -48 + -20 + 30x = 11(2x + -3) * 3x Combine like terms: -48 + -20 = -68 -68 + 30x = 11(2x + -3) * 3x Reorder the terms: -68 + 30x = 11(-3 + 2x) * 3x Reorder the terms for easier multiplication: -68 + 30x = 11 * 3x(-3 + 2x) Multiply 11 * 3 -68 + 30x = 33x(-3 + 2x) -68 + 30x = (-3 * 33x + 2x * 33x) -68 + 30x = (-99x + 66x2) Solving -68 + 30x = -99x + 66x2 Solving for variable 'x'. Combine like terms: 30x + 99x = 129x -68 + 129x + -66x2 = -99x + 66x2 + 99x + -66x2 Reorder the terms: -68 + 129x + -66x2 = -99x + 99x + 66x2 + -66x2 Combine like terms: -99x + 99x = 0 -68 + 129x + -66x2 = 0 + 66x2 + -66x2 -68 + 129x + -66x2 = 66x2 + -66x2 Combine like terms: 66x2 + -66x2 = 0 -68 + 129x + -66x2 = 0 Begin completing the square. Divide all terms by -66 the coefficient of the squared term: Divide each side by '-66'. 1.03030303 + -1.954545455x + x2 = 0 Move the constant term to the right: Add '-1.03030303' to each side of the equation. 1.03030303 + -1.954545455x + -1.03030303 + x2 = 0 + -1.03030303 Reorder the terms: 1.03030303 + -1.03030303 + -1.954545455x + x2 = 0 + -1.03030303 Combine like terms: 1.03030303 + -1.03030303 = 0.00000000 0.00000000 + -1.954545455x + x2 = 0 + -1.03030303 -1.954545455x + x2 = 0 + -1.03030303 Combine like terms: 0 + -1.03030303 = -1.03030303 -1.954545455x + x2 = -1.03030303 The x term is -1.954545455x. Take half its coefficient (-0.9772727275). Square it (0.9550619839) and add it to both sides. Add '0.9550619839' to each side of the equation. -1.954545455x + 0.9550619839 + x2 = -1.03030303 + 0.9550619839 Reorder the terms: 0.9550619839 + -1.954545455x + x2 = -1.03030303 + 0.9550619839 Combine like terms: -1.03030303 + 0.9550619839 = -0.0752410461 0.9550619839 + -1.954545455x + x2 = -0.0752410461 Factor a perfect square on the left side: (x + -0.9772727275)(x + -0.9772727275) = -0.0752410461 Can't calculate square root of the right side. The solution to this equation could not be determined.
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