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Simplifying 10x2 + 21 = 3x + -17 Reorder the terms: 21 + 10x2 = 3x + -17 Reorder the terms: 21 + 10x2 = -17 + 3x Solving 21 + 10x2 = -17 + 3x Solving for variable 'x'. Reorder the terms: 21 + 17 + -3x + 10x2 = -17 + 3x + 17 + -3x Combine like terms: 21 + 17 = 38 38 + -3x + 10x2 = -17 + 3x + 17 + -3x Reorder the terms: 38 + -3x + 10x2 = -17 + 17 + 3x + -3x Combine like terms: -17 + 17 = 0 38 + -3x + 10x2 = 0 + 3x + -3x 38 + -3x + 10x2 = 3x + -3x Combine like terms: 3x + -3x = 0 38 + -3x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 3.8 + -0.3x + x2 = 0 Move the constant term to the right: Add '-3.8' to each side of the equation. 3.8 + -0.3x + -3.8 + x2 = 0 + -3.8 Reorder the terms: 3.8 + -3.8 + -0.3x + x2 = 0 + -3.8 Combine like terms: 3.8 + -3.8 = 0.0 0.0 + -0.3x + x2 = 0 + -3.8 -0.3x + x2 = 0 + -3.8 Combine like terms: 0 + -3.8 = -3.8 -0.3x + x2 = -3.8 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = -3.8 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = -3.8 + 0.0225 Combine like terms: -3.8 + 0.0225 = -3.7775 0.0225 + -0.3x + x2 = -3.7775 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = -3.7775 Can't calculate square root of the right side. The solution to this equation could not be determined.
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