Question

Solve the quadratic equation by factoring

Answer 1

x = 24 ; x = 7

Explanation:

(x - 4)(x - 9) = x*x + (-9) *x + (-4)*x + (-4)*(-9)

= x² - 9x - 4x + 36

=x² - 13x + 36

`(2)/(x -4)+(1)/(x-9)=(1)/(6)\\\\(2*(x-9))/((x-4)(x-9)))+(1*(x-4))/((x-9)(x-4))=(1)/(6)\\\\(2x - 18 +x -4)/((x-4)(x-9))=(1)/(6)\\\\(3x-22)/(x^(2)-13x+36)=(1)/(6)\\\\6*(3x-22)=1*(x^(2)-13x+36)\\\\6*3x - 6*22 = x^(2) - 13x + 36\\\\18x - 132 = x^(2) -13x + 36\\\\0= x^(2) - 13x + 36 - 18x + 132\\\\x^(2) -13x - 18x + 36 + 132 =0\\\\x^(2) - 31x + 168 = 0\\`

x² - 24x - 7x + (-7)*(-24) = 0

x(x - 24) - 7(x - 24) = 0

(x -24)(X - 7) = 0

x - 24 = 0 ; x - 7 = 0

x = 24 ; x = 7