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Simplifying f(0) = 0.03x2 + 0.08x + 30.5 Reorder the terms for easier multiplication: 0f = 0.03x2 + 0.08x + 30.5 Anything times zero is zero. 0f = 0.03x2 + 0.08x + 30.5 Reorder the terms: 0 = 30.5 + 0.08x + 0.03x2 Solving 0 = 30.5 + 0.08x + 0.03x2 Solving for variable 'x'. Combine like terms: 0 + -30.5 = -30.5 -30.5 + -0.08x + -0.03x2 = 30.5 + 0.08x + 0.03x2 + -30.5 + -0.08x + -0.03x2 Reorder the terms: -30.5 + -0.08x + -0.03x2 = 30.5 + -30.5 + 0.08x + -0.08x + 0.03x2 + -0.03x2 Combine like terms: 30.5 + -30.5 = 0.0 -30.5 + -0.08x + -0.03x2 = 0.0 + 0.08x + -0.08x + 0.03x2 + -0.03x2 -30.5 + -0.08x + -0.03x2 = 0.08x + -0.08x + 0.03x2 + -0.03x2 Combine like terms: 0.08x + -0.08x = 0.00 -30.5 + -0.08x + -0.03x2 = 0.00 + 0.03x2 + -0.03x2 -30.5 + -0.08x + -0.03x2 = 0.03x2 + -0.03x2 Combine like terms: 0.03x2 + -0.03x2 = 0.00 -30.5 + -0.08x + -0.03x2 = 0.00 Begin completing the square. Divide all terms by -0.03 the coefficient of the squared term: Divide each side by '-0.03'. 1016.666667 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '-1016.666667' to each side of the equation. 1016.666667 + 2.666666667x + -1016.666667 + x2 = 0 + -1016.666667 Reorder the terms: 1016.666667 + -1016.666667 + 2.666666667x + x2 = 0 + -1016.666667 Combine like terms: 1016.666667 + -1016.666667 = 0.000000 0.000000 + 2.666666667x + x2 = 0 + -1016.666667 2.666666667x + x2 = 0 + -1016.666667 Combine like terms: 0 + -1016.666667 = -1016.666667 2.666666667x + x2 = -1016.666667 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = -1016.666667 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = -1016.666667 + 1.777777780 Combine like terms: -1016.666667 + 1.777777780 = -1014.88888922 1.777777780 + 2.666666667x + x2 = -1014.88888922 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = -1014.88888922 Can't calculate square root of the right side. The solution to this equation could not be determined.
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