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Simplifying 14x2 + 45 = 8x + 4x2 Reorder the terms: 45 + 14x2 = 8x + 4x2 Solving 45 + 14x2 = 8x + 4x2 Solving for variable 'x'. Reorder the terms: 45 + -8x + 14x2 + -4x2 = 8x + 4x2 + -8x + -4x2 Combine like terms: 14x2 + -4x2 = 10x2 45 + -8x + 10x2 = 8x + 4x2 + -8x + -4x2 Reorder the terms: 45 + -8x + 10x2 = 8x + -8x + 4x2 + -4x2 Combine like terms: 8x + -8x = 0 45 + -8x + 10x2 = 0 + 4x2 + -4x2 45 + -8x + 10x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 45 + -8x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 4.5 + -0.8x + x2 = 0.0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -0.8x + -4.5 + x2 = 0.0 + -4.5 Reorder the terms: 4.5 + -4.5 + -0.8x + x2 = 0.0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -0.8x + x2 = 0.0 + -4.5 -0.8x + x2 = 0.0 + -4.5 Combine like terms: 0.0 + -4.5 = -4.5 -0.8x + x2 = -4.5 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = -4.5 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = -4.5 + 0.16 Combine like terms: -4.5 + 0.16 = -4.34 0.16 + -0.8x + x2 = -4.34 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = -4.34 Can't calculate square root of the right side. The solution to this equation could not be determined.
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