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Simplifying 0.5x2 + 3 = -4x2 + 24x + -35 Reorder the terms: 3 + 0.5x2 = -4x2 + 24x + -35 Reorder the terms: 3 + 0.5x2 = -35 + 24x + -4x2 Solving 3 + 0.5x2 = -35 + 24x + -4x2 Solving for variable 'x'. Reorder the terms: 3 + 35 + -24x + 0.5x2 + 4x2 = -35 + 24x + -4x2 + 35 + -24x + 4x2 Combine like terms: 3 + 35 = 38 38 + -24x + 0.5x2 + 4x2 = -35 + 24x + -4x2 + 35 + -24x + 4x2 Combine like terms: 0.5x2 + 4x2 = 4.5x2 38 + -24x + 4.5x2 = -35 + 24x + -4x2 + 35 + -24x + 4x2 Reorder the terms: 38 + -24x + 4.5x2 = -35 + 35 + 24x + -24x + -4x2 + 4x2 Combine like terms: -35 + 35 = 0 38 + -24x + 4.5x2 = 0 + 24x + -24x + -4x2 + 4x2 38 + -24x + 4.5x2 = 24x + -24x + -4x2 + 4x2 Combine like terms: 24x + -24x = 0 38 + -24x + 4.5x2 = 0 + -4x2 + 4x2 38 + -24x + 4.5x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 38 + -24x + 4.5x2 = 0 Begin completing the square. Divide all terms by 4.5 the coefficient of the squared term: Divide each side by '4.5'. 8.444444444 + -5.333333333x + x2 = 0 Move the constant term to the right: Add '-8.444444444' to each side of the equation. 8.444444444 + -5.333333333x + -8.444444444 + x2 = 0 + -8.444444444 Reorder the terms: 8.444444444 + -8.444444444 + -5.333333333x + x2 = 0 + -8.444444444 Combine like terms: 8.444444444 + -8.444444444 = 0.000000000 0.000000000 + -5.333333333x + x2 = 0 + -8.444444444 -5.333333333x + x2 = 0 + -8.444444444 Combine like terms: 0 + -8.444444444 = -8.444444444 -5.333333333x + x2 = -8.444444444 The x term is -5.333333333x. Take half its coefficient (-2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. -5.333333333x + 7.111111113 + x2 = -8.444444444 + 7.111111113 Reorder the terms: 7.111111113 + -5.333333333x + x2 = -8.444444444 + 7.111111113 Combine like terms: -8.444444444 + 7.111111113 = -1.333333331 7.111111113 + -5.333333333x + x2 = -1.333333331 Factor a perfect square on the left side: (x + -2.666666667)(x + -2.666666667) = -1.333333331 Can't calculate square root of the right side. The solution to this equation could not be determined.
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