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Simplifying 0 = 0.4x2 + 2x + 7 Reorder the terms: 0 = 7 + 2x + 0.4x2 Solving 0 = 7 + 2x + 0.4x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + -2x + -0.4x2 = 7 + 2x + 0.4x2 + -7 + -2x + -0.4x2 Reorder the terms: -7 + -2x + -0.4x2 = 7 + -7 + 2x + -2x + 0.4x2 + -0.4x2 Combine like terms: 7 + -7 = 0 -7 + -2x + -0.4x2 = 0 + 2x + -2x + 0.4x2 + -0.4x2 -7 + -2x + -0.4x2 = 2x + -2x + 0.4x2 + -0.4x2 Combine like terms: 2x + -2x = 0 -7 + -2x + -0.4x2 = 0 + 0.4x2 + -0.4x2 -7 + -2x + -0.4x2 = 0.4x2 + -0.4x2 Combine like terms: 0.4x2 + -0.4x2 = 0.0 -7 + -2x + -0.4x2 = 0.0 Begin completing the square. Divide all terms by -0.4 the coefficient of the squared term: Divide each side by '-0.4'. 17.5 + 5x + x2 = 0 Move the constant term to the right: Add '-17.5' to each side of the equation. 17.5 + 5x + -17.5 + x2 = 0 + -17.5 Reorder the terms: 17.5 + -17.5 + 5x + x2 = 0 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + 5x + x2 = 0 + -17.5 5x + x2 = 0 + -17.5 Combine like terms: 0 + -17.5 = -17.5 5x + x2 = -17.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -17.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -17.5 + 6.25 Combine like terms: -17.5 + 6.25 = -11.25 6.25 + 5x + x2 = -11.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -11.25 Can't calculate square root of the right side. The solution to this equation could not be determined.
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