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Simplifying 4x2 + 21x = 5x + -25 Reorder the terms: 21x + 4x2 = 5x + -25 Reorder the terms: 21x + 4x2 = -25 + 5x Solving 21x + 4x2 = -25 + 5x Solving for variable 'x'. Reorder the terms: 25 + 21x + -5x + 4x2 = -25 + 5x + 25 + -5x Combine like terms: 21x + -5x = 16x 25 + 16x + 4x2 = -25 + 5x + 25 + -5x Reorder the terms: 25 + 16x + 4x2 = -25 + 25 + 5x + -5x Combine like terms: -25 + 25 = 0 25 + 16x + 4x2 = 0 + 5x + -5x 25 + 16x + 4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 25 + 16x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.25 + 4x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + 4x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + 4x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + 4x + x2 = 0 + -6.25 4x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 4x + x2 = -6.25 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -6.25 + 4 Reorder the terms: 4 + 4x + x2 = -6.25 + 4 Combine like terms: -6.25 + 4 = -2.25 4 + 4x + x2 = -2.25 Factor a perfect square on the left side: (x + 2)(x + 2) = -2.25 Can't calculate square root of the right side. The solution to this equation could not be determined.
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