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Simplifying 457 = 3.5x2 + -32.9x + 975 Reorder the terms: 457 = 975 + -32.9x + 3.5x2 Solving 457 = 975 + -32.9x + 3.5x2 Solving for variable 'x'. Combine like terms: 457 + -975 = -518 -518 + 32.9x + -3.5x2 = 975 + -32.9x + 3.5x2 + -975 + 32.9x + -3.5x2 Reorder the terms: -518 + 32.9x + -3.5x2 = 975 + -975 + -32.9x + 32.9x + 3.5x2 + -3.5x2 Combine like terms: 975 + -975 = 0 -518 + 32.9x + -3.5x2 = 0 + -32.9x + 32.9x + 3.5x2 + -3.5x2 -518 + 32.9x + -3.5x2 = -32.9x + 32.9x + 3.5x2 + -3.5x2 Combine like terms: -32.9x + 32.9x = 0.0 -518 + 32.9x + -3.5x2 = 0.0 + 3.5x2 + -3.5x2 -518 + 32.9x + -3.5x2 = 3.5x2 + -3.5x2 Combine like terms: 3.5x2 + -3.5x2 = 0.0 -518 + 32.9x + -3.5x2 = 0.0 Begin completing the square. Divide all terms by -3.5 the coefficient of the squared term: Divide each side by '-3.5'. 148 + -9.4x + x2 = 0 Move the constant term to the right: Add '-148' to each side of the equation. 148 + -9.4x + -148 + x2 = 0 + -148 Reorder the terms: 148 + -148 + -9.4x + x2 = 0 + -148 Combine like terms: 148 + -148 = 0 0 + -9.4x + x2 = 0 + -148 -9.4x + x2 = 0 + -148 Combine like terms: 0 + -148 = -148 -9.4x + x2 = -148 The x term is -9.4x. Take half its coefficient (-4.7). Square it (22.09) and add it to both sides. Add '22.09' to each side of the equation. -9.4x + 22.09 + x2 = -148 + 22.09 Reorder the terms: 22.09 + -9.4x + x2 = -148 + 22.09 Combine like terms: -148 + 22.09 = -125.91 22.09 + -9.4x + x2 = -125.91 Factor a perfect square on the left side: (x + -4.7)(x + -4.7) = -125.91 Can't calculate square root of the right side. The solution to this equation could not be determined.
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