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Simplifying x(x + 7) = 15x + -21 Reorder the terms: x(7 + x) = 15x + -21 (7 * x + x * x) = 15x + -21 (7x + x2) = 15x + -21 Reorder the terms: 7x + x2 = -21 + 15x Solving 7x + x2 = -21 + 15x Solving for variable 'x'. Reorder the terms: 21 + 7x + -15x + x2 = -21 + 15x + 21 + -15x Combine like terms: 7x + -15x = -8x 21 + -8x + x2 = -21 + 15x + 21 + -15x Reorder the terms: 21 + -8x + x2 = -21 + 21 + 15x + -15x Combine like terms: -21 + 21 = 0 21 + -8x + x2 = 0 + 15x + -15x 21 + -8x + x2 = 15x + -15x Combine like terms: 15x + -15x = 0 21 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -8x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + -8x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -8x + x2 = 0 + -21 -8x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 -8x + x2 = -21 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -21 + 16 Reorder the terms: 16 + -8x + x2 = -21 + 16 Combine like terms: -21 + 16 = -5 16 + -8x + x2 = -5 Factor a perfect square on the left side: (x + -4)(x + -4) = -5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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