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Simplifying 0 = 0.5x2 + -8x + 35 Reorder the terms: 0 = 35 + -8x + 0.5x2 Solving 0 = 35 + -8x + 0.5x2 Solving for variable 'x'. Combine like terms: 0 + -35 = -35 -35 + 8x + -0.5x2 = 35 + -8x + 0.5x2 + -35 + 8x + -0.5x2 Reorder the terms: -35 + 8x + -0.5x2 = 35 + -35 + -8x + 8x + 0.5x2 + -0.5x2 Combine like terms: 35 + -35 = 0 -35 + 8x + -0.5x2 = 0 + -8x + 8x + 0.5x2 + -0.5x2 -35 + 8x + -0.5x2 = -8x + 8x + 0.5x2 + -0.5x2 Combine like terms: -8x + 8x = 0 -35 + 8x + -0.5x2 = 0 + 0.5x2 + -0.5x2 -35 + 8x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 -35 + 8x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 70 + -16x + x2 = 0 Move the constant term to the right: Add '-70' to each side of the equation. 70 + -16x + -70 + x2 = 0 + -70 Reorder the terms: 70 + -70 + -16x + x2 = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -16x + x2 = 0 + -70 -16x + x2 = 0 + -70 Combine like terms: 0 + -70 = -70 -16x + x2 = -70 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -70 + 64 Reorder the terms: 64 + -16x + x2 = -70 + 64 Combine like terms: -70 + 64 = -6 64 + -16x + x2 = -6 Factor a perfect square on the left side: (x + -8)(x + -8) = -6 Can't calculate square root of the right side. The solution to this equation could not be determined.
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