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Simplifying x2 + 2x(1 + -1x) = 84 x2 + (1 * 2x + -1x * 2x) = 84 x2 + (2x + -2x2) = 84 Reorder the terms: 2x + x2 + -2x2 = 84 Combine like terms: x2 + -2x2 = -1x2 2x + -1x2 = 84 Solving 2x + -1x2 = 84 Solving for variable 'x'. Reorder the terms: -84 + 2x + -1x2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 84 + -2x + x2 = 0 Move the constant term to the right: Add '-84' to each side of the equation. 84 + -2x + -84 + x2 = 0 + -84 Reorder the terms: 84 + -84 + -2x + x2 = 0 + -84 Combine like terms: 84 + -84 = 0 0 + -2x + x2 = 0 + -84 -2x + x2 = 0 + -84 Combine like terms: 0 + -84 = -84 -2x + x2 = -84 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -84 + 1 Reorder the terms: 1 + -2x + x2 = -84 + 1 Combine like terms: -84 + 1 = -83 1 + -2x + x2 = -83 Factor a perfect square on the left side: (x + -1)(x + -1) = -83 Can't calculate square root of the right side. The solution to this equation could not be determined.
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