Now, we have a quadratic equation in standard form:
x^2 - 4x - 4 = 0
To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, the equation does not factor easily, so we will use the quadratic formula:
x = (-(-4) ± sqrt((-4)^2 - 41(-4))) / 2*1 x = (4 ± sqrt(16 + 16)) / 2 x = (4 ± sqrt(32)) / 2 x = (4 ± 4√2) / 2 x = 2 ± 2√2
To solve this equation, we first need to distribute and simplify on both sides:
(x-3)(x+5) - 6(x-3) - 7 = 0
(x^2 + 2x - 15) - (6x - 18) - 7 = 0
x^2 + 2x - 15 - 6x + 18 - 7 = 0
x^2 - 4x - 4 = 0
Now, we have a quadratic equation in standard form:
x^2 - 4x - 4 = 0
To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, the equation does not factor easily, so we will use the quadratic formula:
x = (-(-4) ± sqrt((-4)^2 - 41(-4))) / 2*1
x = (4 ± sqrt(16 + 16)) / 2
x = (4 ± sqrt(32)) / 2
x = (4 ± 4√2) / 2
x = 2 ± 2√2
Therefore, the two solutions to the equation are:
x = 2 + 2√2 or x = 2 - 2√2