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Simplifying 0 = 0.25x2 + 1.5x + 7 Reorder the terms: 0 = 7 + 1.5x + 0.25x2 Solving 0 = 7 + 1.5x + 0.25x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + -1.5x + -0.25x2 = 7 + 1.5x + 0.25x2 + -7 + -1.5x + -0.25x2 Reorder the terms: -7 + -1.5x + -0.25x2 = 7 + -7 + 1.5x + -1.5x + 0.25x2 + -0.25x2 Combine like terms: 7 + -7 = 0 -7 + -1.5x + -0.25x2 = 0 + 1.5x + -1.5x + 0.25x2 + -0.25x2 -7 + -1.5x + -0.25x2 = 1.5x + -1.5x + 0.25x2 + -0.25x2 Combine like terms: 1.5x + -1.5x = 0.0 -7 + -1.5x + -0.25x2 = 0.0 + 0.25x2 + -0.25x2 -7 + -1.5x + -0.25x2 = 0.25x2 + -0.25x2 Combine like terms: 0.25x2 + -0.25x2 = 0.00 -7 + -1.5x + -0.25x2 = 0.00 Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. 28 + 6x + x2 = 0 Move the constant term to the right: Add '-28' to each side of the equation. 28 + 6x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + 6x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + 6x + x2 = 0 + -28 6x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 6x + x2 = -28 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -28 + 9 Reorder the terms: 9 + 6x + x2 = -28 + 9 Combine like terms: -28 + 9 = -19 9 + 6x + x2 = -19 Factor a perfect square on the left side: (x + 3)(x + 3) = -19 Can't calculate square root of the right side. The solution to this equation could not be determined.
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