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Simplifying (x + 7)(x + -3) = x2 + 1 Reorder the terms: (7 + x)(x + -3) = x2 + 1 Reorder the terms: (7 + x)(-3 + x) = x2 + 1 Multiply (7 + x) * (-3 + x) (7(-3 + x) + x(-3 + x)) = x2 + 1 ((-3 * 7 + x * 7) + x(-3 + x)) = x2 + 1 ((-21 + 7x) + x(-3 + x)) = x2 + 1 (-21 + 7x + (-3 * x + x * x)) = x2 + 1 (-21 + 7x + (-3x + x2)) = x2 + 1 Combine like terms: 7x + -3x = 4x (-21 + 4x + x2) = x2 + 1 Reorder the terms: -21 + 4x + x2 = 1 + x2 Add '-1x2' to each side of the equation. -21 + 4x + x2 + -1x2 = 1 + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -21 + 4x + 0 = 1 + x2 + -1x2 -21 + 4x = 1 + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -21 + 4x = 1 + 0 -21 + 4x = 1 Solving -21 + 4x = 1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + 4x = 1 + 21 Combine like terms: -21 + 21 = 0 0 + 4x = 1 + 21 4x = 1 + 21 Combine like terms: 1 + 21 = 22 4x = 22 Divide each side by '4'. x = 5.5 Simplifying x = 5.5
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