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Simplifying 0 = 27x2 + -49x + 53 Reorder the terms: 0 = 53 + -49x + 27x2 Solving 0 = 53 + -49x + 27x2 Solving for variable 'x'. Combine like terms: 0 + -53 = -53 -53 + 49x + -27x2 = 53 + -49x + 27x2 + -53 + 49x + -27x2 Reorder the terms: -53 + 49x + -27x2 = 53 + -53 + -49x + 49x + 27x2 + -27x2 Combine like terms: 53 + -53 = 0 -53 + 49x + -27x2 = 0 + -49x + 49x + 27x2 + -27x2 -53 + 49x + -27x2 = -49x + 49x + 27x2 + -27x2 Combine like terms: -49x + 49x = 0 -53 + 49x + -27x2 = 0 + 27x2 + -27x2 -53 + 49x + -27x2 = 27x2 + -27x2 Combine like terms: 27x2 + -27x2 = 0 -53 + 49x + -27x2 = 0 Begin completing the square. Divide all terms by -27 the coefficient of the squared term: Divide each side by '-27'. 1.962962963 + -1.814814815x + x2 = 0 Move the constant term to the right: Add '-1.962962963' to each side of the equation. 1.962962963 + -1.814814815x + -1.962962963 + x2 = 0 + -1.962962963 Reorder the terms: 1.962962963 + -1.962962963 + -1.814814815x + x2 = 0 + -1.962962963 Combine like terms: 1.962962963 + -1.962962963 = 0.000000000 0.000000000 + -1.814814815x + x2 = 0 + -1.962962963 -1.814814815x + x2 = 0 + -1.962962963 Combine like terms: 0 + -1.962962963 = -1.962962963 -1.814814815x + x2 = -1.962962963 The x term is -1.814814815x. Take half its coefficient (-0.9074074075). Square it (0.8233882032) and add it to both sides. Add '0.8233882032' to each side of the equation. -1.814814815x + 0.8233882032 + x2 = -1.962962963 + 0.8233882032 Reorder the terms: 0.8233882032 + -1.814814815x + x2 = -1.962962963 + 0.8233882032 Combine like terms: -1.962962963 + 0.8233882032 = -1.1395747598 0.8233882032 + -1.814814815x + x2 = -1.1395747598 Factor a perfect square on the left side: (x + -0.9074074075)(x + -0.9074074075) = -1.1395747598 Can't calculate square root of the right side. The solution to this equation could not be determined.
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