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Simplifying 7x2 + -2x + 3 = 5x2 + -10 Reorder the terms: 3 + -2x + 7x2 = 5x2 + -10 Reorder the terms: 3 + -2x + 7x2 = -10 + 5x2 Solving 3 + -2x + 7x2 = -10 + 5x2 Solving for variable 'x'. Reorder the terms: 3 + 10 + -2x + 7x2 + -5x2 = -10 + 5x2 + 10 + -5x2 Combine like terms: 3 + 10 = 13 13 + -2x + 7x2 + -5x2 = -10 + 5x2 + 10 + -5x2 Combine like terms: 7x2 + -5x2 = 2x2 13 + -2x + 2x2 = -10 + 5x2 + 10 + -5x2 Reorder the terms: 13 + -2x + 2x2 = -10 + 10 + 5x2 + -5x2 Combine like terms: -10 + 10 = 0 13 + -2x + 2x2 = 0 + 5x2 + -5x2 13 + -2x + 2x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 13 + -2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6.5 + -1x + x2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -1x + -6.5 + x2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -1x + x2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -1x + x2 = 0 + -6.5 -1x + x2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -1x + x2 = -6.5 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 = -6.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -6.5 + 0.25 Combine like terms: -6.5 + 0.25 = -6.25 0.25 + -1x + x2 = -6.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -6.25 Can't calculate square root of the right side. The solution to this equation could not be determined.
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