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Simplifying 5x2 + -23x = -102 Reorder the terms: -23x + 5x2 = -102 Solving -23x + 5x2 = -102 Solving for variable 'x'. Reorder the terms: 102 + -23x + 5x2 = -102 + 102 Combine like terms: -102 + 102 = 0 102 + -23x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 20.4 + -4.6x + x2 = 0 Move the constant term to the right: Add '-20.4' to each side of the equation. 20.4 + -4.6x + -20.4 + x2 = 0 + -20.4 Reorder the terms: 20.4 + -20.4 + -4.6x + x2 = 0 + -20.4 Combine like terms: 20.4 + -20.4 = 0.0 0.0 + -4.6x + x2 = 0 + -20.4 -4.6x + x2 = 0 + -20.4 Combine like terms: 0 + -20.4 = -20.4 -4.6x + x2 = -20.4 The x term is -4.6x. Take half its coefficient (-2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. -4.6x + 5.29 + x2 = -20.4 + 5.29 Reorder the terms: 5.29 + -4.6x + x2 = -20.4 + 5.29 Combine like terms: -20.4 + 5.29 = -15.11 5.29 + -4.6x + x2 = -15.11 Factor a perfect square on the left side: (x + -2.3)(x + -2.3) = -15.11 Can't calculate square root of the right side. The solution to this equation could not be determined.
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