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Simplifying 100 = 0.03x2 + -33x + 15000 Reorder the terms: 100 = 15000 + -33x + 0.03x2 Solving 100 = 15000 + -33x + 0.03x2 Solving for variable 'x'. Combine like terms: 100 + -15000 = -14900 -14900 + 33x + -0.03x2 = 15000 + -33x + 0.03x2 + -15000 + 33x + -0.03x2 Reorder the terms: -14900 + 33x + -0.03x2 = 15000 + -15000 + -33x + 33x + 0.03x2 + -0.03x2 Combine like terms: 15000 + -15000 = 0 -14900 + 33x + -0.03x2 = 0 + -33x + 33x + 0.03x2 + -0.03x2 -14900 + 33x + -0.03x2 = -33x + 33x + 0.03x2 + -0.03x2 Combine like terms: -33x + 33x = 0 -14900 + 33x + -0.03x2 = 0 + 0.03x2 + -0.03x2 -14900 + 33x + -0.03x2 = 0.03x2 + -0.03x2 Combine like terms: 0.03x2 + -0.03x2 = 0.00 -14900 + 33x + -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'. 496666.6667 + -1100x + x2 = 0 Move the constant term to the right: Add '-496666.6667' to each side of the equation. 496666.6667 + -1100x + -496666.6667 + x2 = 0 + -496666.6667 Reorder the terms: 496666.6667 + -496666.6667 + -1100x + x2 = 0 + -496666.6667 Combine like terms: 496666.6667 + -496666.6667 = 0.0000 0.0000 + -1100x + x2 = 0 + -496666.6667 -1100x + x2 = 0 + -496666.6667 Combine like terms: 0 + -496666.6667 = -496666.6667 -1100x + x2 = -496666.6667 The x term is -1100x. Take half its coefficient (-550). Square it (302500) and add it to both sides. Add '302500' to each side of the equation. -1100x + 302500 + x2 = -496666.6667 + 302500 Reorder the terms: 302500 + -1100x + x2 = -496666.6667 + 302500 Combine like terms: -496666.6667 + 302500 = -194166.6667 302500 + -1100x + x2 = -194166.6667 Factor a perfect square on the left side: (x + -550)(x + -550) = -194166.6667 Can't calculate square root of the right side. The solution to this equation could not be determined.
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