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Simplifying 5x2 + 8x + 21 = 4x2 + 6x + -19 Reorder the terms: 21 + 8x + 5x2 = 4x2 + 6x + -19 Reorder the terms: 21 + 8x + 5x2 = -19 + 6x + 4x2 Solving 21 + 8x + 5x2 = -19 + 6x + 4x2 Solving for variable 'x'. Reorder the terms: 21 + 19 + 8x + -6x + 5x2 + -4x2 = -19 + 6x + 4x2 + 19 + -6x + -4x2 Combine like terms: 21 + 19 = 40 40 + 8x + -6x + 5x2 + -4x2 = -19 + 6x + 4x2 + 19 + -6x + -4x2 Combine like terms: 8x + -6x = 2x 40 + 2x + 5x2 + -4x2 = -19 + 6x + 4x2 + 19 + -6x + -4x2 Combine like terms: 5x2 + -4x2 = 1x2 40 + 2x + 1x2 = -19 + 6x + 4x2 + 19 + -6x + -4x2 Reorder the terms: 40 + 2x + 1x2 = -19 + 19 + 6x + -6x + 4x2 + -4x2 Combine like terms: -19 + 19 = 0 40 + 2x + 1x2 = 0 + 6x + -6x + 4x2 + -4x2 40 + 2x + 1x2 = 6x + -6x + 4x2 + -4x2 Combine like terms: 6x + -6x = 0 40 + 2x + 1x2 = 0 + 4x2 + -4x2 40 + 2x + 1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 40 + 2x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + 2x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + 2x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 2x + x2 = 0 + -40 2x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 2x + x2 = -40 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 = -40 + 1 Reorder the terms: 1 + 2x + x2 = -40 + 1 Combine like terms: -40 + 1 = -39 1 + 2x + x2 = -39 Factor a perfect square on the left side: (x + 1)(x + 1) = -39 Can't calculate square root of the right side. The solution to this equation could not be determined.
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