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Simplifying 5x2 + -2x + 37 = x2 + 2x Reorder the terms: 37 + -2x + 5x2 = x2 + 2x Reorder the terms: 37 + -2x + 5x2 = 2x + x2 Solving 37 + -2x + 5x2 = 2x + x2 Solving for variable 'x'. Reorder the terms: 37 + -2x + -2x + 5x2 + -1x2 = 2x + x2 + -2x + -1x2 Combine like terms: -2x + -2x = -4x 37 + -4x + 5x2 + -1x2 = 2x + x2 + -2x + -1x2 Combine like terms: 5x2 + -1x2 = 4x2 37 + -4x + 4x2 = 2x + x2 + -2x + -1x2 Reorder the terms: 37 + -4x + 4x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 37 + -4x + 4x2 = 0 + x2 + -1x2 37 + -4x + 4x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 37 + -4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 9.25 + -1x + x2 = 0 Move the constant term to the right: Add '-9.25' to each side of the equation. 9.25 + -1x + -9.25 + x2 = 0 + -9.25 Reorder the terms: 9.25 + -9.25 + -1x + x2 = 0 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + -1x + x2 = 0 + -9.25 -1x + x2 = 0 + -9.25 Combine like terms: 0 + -9.25 = -9.25 -1x + x2 = -9.25 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -9.25 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -9.25 + 0.25 Combine like terms: -9.25 + 0.25 = -9 0.25 + -1x + x2 = -9 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -9 Can't calculate square root of the right side. The solution to this equation could not be determined.
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