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Simplifying 0 = 5x4 + -24x2 + 144 Reorder the terms: 0 = 144 + -24x2 + 5x4 Solving 0 = 144 + -24x2 + 5x4 Solving for variable 'x'. Combine like terms: 0 + -144 = -144 -144 + 24x2 + -5x4 = 144 + -24x2 + 5x4 + -144 + 24x2 + -5x4 Reorder the terms: -144 + 24x2 + -5x4 = 144 + -144 + -24x2 + 24x2 + 5x4 + -5x4 Combine like terms: 144 + -144 = 0 -144 + 24x2 + -5x4 = 0 + -24x2 + 24x2 + 5x4 + -5x4 -144 + 24x2 + -5x4 = -24x2 + 24x2 + 5x4 + -5x4 Combine like terms: -24x2 + 24x2 = 0 -144 + 24x2 + -5x4 = 0 + 5x4 + -5x4 -144 + 24x2 + -5x4 = 5x4 + -5x4 Combine like terms: 5x4 + -5x4 = 0 -144 + 24x2 + -5x4 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 28.8 + -4.8x2 + x4 = 0 Move the constant term to the right: Add '-28.8' to each side of the equation. 28.8 + -4.8x2 + -28.8 + x4 = 0 + -28.8 Reorder the terms: 28.8 + -28.8 + -4.8x2 + x4 = 0 + -28.8 Combine like terms: 28.8 + -28.8 = 0.0 0.0 + -4.8x2 + x4 = 0 + -28.8 -4.8x2 + x4 = 0 + -28.8 Combine like terms: 0 + -28.8 = -28.8 -4.8x2 + x4 = -28.8 The x term is -4.8x2. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8x2 + 5.76 + x4 = -28.8 + 5.76 Reorder the terms: 5.76 + -4.8x2 + x4 = -28.8 + 5.76 Combine like terms: -28.8 + 5.76 = -23.04 5.76 + -4.8x2 + x4 = -23.04 Factor a perfect square on the left side: (x2 + -2.4)(x2 + -2.4) = -23.04 Can't calculate square root of the right side. The solution to this equation could not be determined.
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