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Simplifying 21 + 3x = x(-5x + 4) Reorder the terms: 21 + 3x = x(4 + -5x) 21 + 3x = (4 * x + -5x * x) 21 + 3x = (4x + -5x2) Solving 21 + 3x = 4x + -5x2 Solving for variable 'x'. Combine like terms: 3x + -4x = -1x 21 + -1x + 5x2 = 4x + -5x2 + -4x + 5x2 Reorder the terms: 21 + -1x + 5x2 = 4x + -4x + -5x2 + 5x2 Combine like terms: 4x + -4x = 0 21 + -1x + 5x2 = 0 + -5x2 + 5x2 21 + -1x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 21 + -1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4.2 + -0.2x + x2 = 0 Move the constant term to the right: Add '-4.2' to each side of the equation. 4.2 + -0.2x + -4.2 + x2 = 0 + -4.2 Reorder the terms: 4.2 + -4.2 + -0.2x + x2 = 0 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + -0.2x + x2 = 0 + -4.2 -0.2x + x2 = 0 + -4.2 Combine like terms: 0 + -4.2 = -4.2 -0.2x + x2 = -4.2 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 = -4.2 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = -4.2 + 0.01 Combine like terms: -4.2 + 0.01 = -4.19 0.01 + -0.2x + x2 = -4.19 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = -4.19 Can't calculate square root of the right side. The solution to this equation could not be determined.
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