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Simplifying 0 = -11x2 + 30x + -45 Reorder the terms: 0 = -45 + 30x + -11x2 Solving 0 = -45 + 30x + -11x2 Solving for variable 'x'. Combine like terms: 0 + 45 = 45 45 + -30x + 11x2 = -45 + 30x + -11x2 + 45 + -30x + 11x2 Reorder the terms: 45 + -30x + 11x2 = -45 + 45 + 30x + -30x + -11x2 + 11x2 Combine like terms: -45 + 45 = 0 45 + -30x + 11x2 = 0 + 30x + -30x + -11x2 + 11x2 45 + -30x + 11x2 = 30x + -30x + -11x2 + 11x2 Combine like terms: 30x + -30x = 0 45 + -30x + 11x2 = 0 + -11x2 + 11x2 45 + -30x + 11x2 = -11x2 + 11x2 Combine like terms: -11x2 + 11x2 = 0 45 + -30x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 4.090909091 + -2.727272727x + x2 = 0 Move the constant term to the right: Add '-4.090909091' to each side of the equation. 4.090909091 + -2.727272727x + -4.090909091 + x2 = 0 + -4.090909091 Reorder the terms: 4.090909091 + -4.090909091 + -2.727272727x + x2 = 0 + -4.090909091 Combine like terms: 4.090909091 + -4.090909091 = 0.000000000 0.000000000 + -2.727272727x + x2 = 0 + -4.090909091 -2.727272727x + x2 = 0 + -4.090909091 Combine like terms: 0 + -4.090909091 = -4.090909091 -2.727272727x + x2 = -4.090909091 The x term is -2.727272727x. Take half its coefficient (-1.363636364). Square it (1.859504133) and add it to both sides. Add '1.859504133' to each side of the equation. -2.727272727x + 1.859504133 + x2 = -4.090909091 + 1.859504133 Reorder the terms: 1.859504133 + -2.727272727x + x2 = -4.090909091 + 1.859504133 Combine like terms: -4.090909091 + 1.859504133 = -2.231404958 1.859504133 + -2.727272727x + x2 = -2.231404958 Factor a perfect square on the left side: (x + -1.363636364)(x + -1.363636364) = -2.231404958 Can't calculate square root of the right side. The solution to this equation could not be determined.
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