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Simplifying 3x2 + 8x + 7 = -8x2 + 5 Reorder the terms: 7 + 8x + 3x2 = -8x2 + 5 Reorder the terms: 7 + 8x + 3x2 = 5 + -8x2 Solving 7 + 8x + 3x2 = 5 + -8x2 Solving for variable 'x'. Reorder the terms: 7 + -5 + 8x + 3x2 + 8x2 = 5 + -8x2 + -5 + 8x2 Combine like terms: 7 + -5 = 2 2 + 8x + 3x2 + 8x2 = 5 + -8x2 + -5 + 8x2 Combine like terms: 3x2 + 8x2 = 11x2 2 + 8x + 11x2 = 5 + -8x2 + -5 + 8x2 Reorder the terms: 2 + 8x + 11x2 = 5 + -5 + -8x2 + 8x2 Combine like terms: 5 + -5 = 0 2 + 8x + 11x2 = 0 + -8x2 + 8x2 2 + 8x + 11x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 2 + 8x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.1818181818 + 0.7272727273x + x2 = 0 Move the constant term to the right: Add '-0.1818181818' to each side of the equation. 0.1818181818 + 0.7272727273x + -0.1818181818 + x2 = 0 + -0.1818181818 Reorder the terms: 0.1818181818 + -0.1818181818 + 0.7272727273x + x2 = 0 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + 0.7272727273x + x2 = 0 + -0.1818181818 0.7272727273x + x2 = 0 + -0.1818181818 Combine like terms: 0 + -0.1818181818 = -0.1818181818 0.7272727273x + x2 = -0.1818181818 The x term is 0.7272727273x. Take half its coefficient (0.3636363637). Square it (0.1322314050) and add it to both sides. Add '0.1322314050' to each side of the equation. 0.7272727273x + 0.1322314050 + x2 = -0.1818181818 + 0.1322314050 Reorder the terms: 0.1322314050 + 0.7272727273x + x2 = -0.1818181818 + 0.1322314050 Combine like terms: -0.1818181818 + 0.1322314050 = -0.0495867768 0.1322314050 + 0.7272727273x + x2 = -0.0495867768 Factor a perfect square on the left side: (x + 0.3636363637)(x + 0.3636363637) = -0.0495867768 Can't calculate square root of the right side. The solution to this equation could not be determined.
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