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Simplifying 4z(5z + -2) = -15 + 6 Reorder the terms: 4z(-2 + 5z) = -15 + 6 (-2 * 4z + 5z * 4z) = -15 + 6 (-8z + 20z2) = -15 + 6 Combine like terms: -15 + 6 = -9 -8z + 20z2 = -9 Solving -8z + 20z2 = -9 Solving for variable 'z'. Reorder the terms: 9 + -8z + 20z2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -8z + 20z2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.45 + -0.4z + z2 = 0.0 Move the constant term to the right: Add '-0.45' to each side of the equation. 0.45 + -0.4z + -0.45 + z2 = 0.0 + -0.45 Reorder the terms: 0.45 + -0.45 + -0.4z + z2 = 0.0 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + -0.4z + z2 = 0.0 + -0.45 -0.4z + z2 = 0.0 + -0.45 Combine like terms: 0.0 + -0.45 = -0.45 -0.4z + z2 = -0.45 The z term is -0.4z. 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. -0.4z + 0.04 + z2 = -0.45 + 0.04 Reorder the terms: 0.04 + -0.4z + z2 = -0.45 + 0.04 Combine like terms: -0.45 + 0.04 = -0.41 0.04 + -0.4z + z2 = -0.41 Factor a perfect square on the left side: (z + -0.2)(z + -0.2) = -0.41 Can't calculate square root of the right side. The solution to this equation could not be determined.
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