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Simplifying 10 = -4x2 + 10x + 1 Reorder the terms: 10 = 1 + 10x + -4x2 Solving 10 = 1 + 10x + -4x2 Solving for variable 'x'. Combine like terms: 10 + -1 = 9 9 + -10x + 4x2 = 1 + 10x + -4x2 + -1 + -10x + 4x2 Reorder the terms: 9 + -10x + 4x2 = 1 + -1 + 10x + -10x + -4x2 + 4x2 Combine like terms: 1 + -1 = 0 9 + -10x + 4x2 = 0 + 10x + -10x + -4x2 + 4x2 9 + -10x + 4x2 = 10x + -10x + -4x2 + 4x2 Combine like terms: 10x + -10x = 0 9 + -10x + 4x2 = 0 + -4x2 + 4x2 9 + -10x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 9 + -10x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + -2.5x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -2.5x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -2.5x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -2.5x + x2 = 0 + -2.25 -2.5x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -2.5x + x2 = -2.25 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -2.25 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -2.25 + 1.5625 Combine like terms: -2.25 + 1.5625 = -0.6875 1.5625 + -2.5x + x2 = -0.6875 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = -0.6875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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