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Simplifying 9x2 + -45x + 35 = 6x2 + -30x Reorder the terms: 35 + -45x + 9x2 = 6x2 + -30x Reorder the terms: 35 + -45x + 9x2 = -30x + 6x2 Solving 35 + -45x + 9x2 = -30x + 6x2 Solving for variable 'x'. Reorder the terms: 35 + -45x + 30x + 9x2 + -6x2 = -30x + 6x2 + 30x + -6x2 Combine like terms: -45x + 30x = -15x 35 + -15x + 9x2 + -6x2 = -30x + 6x2 + 30x + -6x2 Combine like terms: 9x2 + -6x2 = 3x2 35 + -15x + 3x2 = -30x + 6x2 + 30x + -6x2 Reorder the terms: 35 + -15x + 3x2 = -30x + 30x + 6x2 + -6x2 Combine like terms: -30x + 30x = 0 35 + -15x + 3x2 = 0 + 6x2 + -6x2 35 + -15x + 3x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 35 + -15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 11.66666667 + -5x + x2 = 0 Move the constant term to the right: Add '-11.66666667' to each side of the equation. 11.66666667 + -5x + -11.66666667 + x2 = 0 + -11.66666667 Reorder the terms: 11.66666667 + -11.66666667 + -5x + x2 = 0 + -11.66666667 Combine like terms: 11.66666667 + -11.66666667 = 0.00000000 0.00000000 + -5x + x2 = 0 + -11.66666667 -5x + x2 = 0 + -11.66666667 Combine like terms: 0 + -11.66666667 = -11.66666667 -5x + x2 = -11.66666667 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -11.66666667 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -11.66666667 + 6.25 Combine like terms: -11.66666667 + 6.25 = -5.41666667 6.25 + -5x + x2 = -5.41666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = -5.41666667 Can't calculate square root of the right side. The solution to this equation could not be determined.
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