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Simplifying 5x + 3 = 12x + -7x2 Reorder the terms: 3 + 5x = 12x + -7x2 Solving 3 + 5x = 12x + -7x2 Solving for variable 'x'. Combine like terms: 5x + -12x = -7x 3 + -7x + 7x2 = 12x + -7x2 + -12x + 7x2 Reorder the terms: 3 + -7x + 7x2 = 12x + -12x + -7x2 + 7x2 Combine like terms: 12x + -12x = 0 3 + -7x + 7x2 = 0 + -7x2 + 7x2 3 + -7x + 7x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 3 + -7x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.4285714286 + -1x + x2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + -1x + -0.4285714286 + x2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + -1x + x2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + -0.4285714286 -1x + x2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 -1x + x2 = -0.4285714286 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 = -0.4285714286 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.4285714286 + 0.25 Combine like terms: -0.4285714286 + 0.25 = -0.1785714286 0.25 + -1x + x2 = -0.1785714286 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -0.1785714286 Can't calculate square root of the right side. The solution to this equation could not be determined.
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