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Simplifying f(0) = 0.01x2 + 0.06x + 31.2 Reorder the terms for easier multiplication: 0f = 0.01x2 + 0.06x + 31.2 Anything times zero is zero. 0f = 0.01x2 + 0.06x + 31.2 Reorder the terms: 0 = 31.2 + 0.06x + 0.01x2 Solving 0 = 31.2 + 0.06x + 0.01x2 Solving for variable 'x'. Combine like terms: 0 + -31.2 = -31.2 -31.2 + -0.06x + -0.01x2 = 31.2 + 0.06x + 0.01x2 + -31.2 + -0.06x + -0.01x2 Reorder the terms: -31.2 + -0.06x + -0.01x2 = 31.2 + -31.2 + 0.06x + -0.06x + 0.01x2 + -0.01x2 Combine like terms: 31.2 + -31.2 = 0.0 -31.2 + -0.06x + -0.01x2 = 0.0 + 0.06x + -0.06x + 0.01x2 + -0.01x2 -31.2 + -0.06x + -0.01x2 = 0.06x + -0.06x + 0.01x2 + -0.01x2 Combine like terms: 0.06x + -0.06x = 0.00 -31.2 + -0.06x + -0.01x2 = 0.00 + 0.01x2 + -0.01x2 -31.2 + -0.06x + -0.01x2 = 0.01x2 + -0.01x2 Combine like terms: 0.01x2 + -0.01x2 = 0.00 -31.2 + -0.06x + -0.01x2 = 0.00 Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. 3120 + 6x + x2 = 0 Move the constant term to the right: Add '-3120' to each side of the equation. 3120 + 6x + -3120 + x2 = 0 + -3120 Reorder the terms: 3120 + -3120 + 6x + x2 = 0 + -3120 Combine like terms: 3120 + -3120 = 0 0 + 6x + x2 = 0 + -3120 6x + x2 = 0 + -3120 Combine like terms: 0 + -3120 = -3120 6x + x2 = -3120 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 = -3120 + 9 Reorder the terms: 9 + 6x + x2 = -3120 + 9 Combine like terms: -3120 + 9 = -3111 9 + 6x + x2 = -3111 Factor a perfect square on the left side: (x + 3)(x + 3) = -3111 Can't calculate square root of the right side. The solution to this equation could not be determined.
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