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Simplifying 5x2 = x + -42 Reorder the terms: 5x2 = -42 + x Solving 5x2 = -42 + x Solving for variable 'x'. Reorder the terms: 42 + -1x + 5x2 = -42 + x + 42 + -1x Reorder the terms: 42 + -1x + 5x2 = -42 + 42 + x + -1x Combine like terms: -42 + 42 = 0 42 + -1x + 5x2 = 0 + x + -1x 42 + -1x + 5x2 = x + -1x Combine like terms: x + -1x = 0 42 + -1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 8.4 + -0.2x + x2 = 0 Move the constant term to the right: Add '-8.4' to each side of the equation. 8.4 + -0.2x + -8.4 + x2 = 0 + -8.4 Reorder the terms: 8.4 + -8.4 + -0.2x + x2 = 0 + -8.4 Combine like terms: 8.4 + -8.4 = 0.0 0.0 + -0.2x + x2 = 0 + -8.4 -0.2x + x2 = 0 + -8.4 Combine like terms: 0 + -8.4 = -8.4 -0.2x + x2 = -8.4 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = -8.4 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = -8.4 + 0.01 Combine like terms: -8.4 + 0.01 = -8.39 0.01 + -0.2x + x2 = -8.39 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = -8.39 Can't calculate square root of the right side. The solution to this equation could not be determined.
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