ANSWER
The solution of the equation is (8, 6)
STEP-BY-STEP EXPLANATION:
The quadratic equation is given below as
[tex]x^2\text{ - 14x + 48 = 0}[/tex]Recall that, the standard form of the quadratic function is given as
[tex]ax^2\text{ + bx + c = 0}[/tex]Relating the two together, we have the following data
• a = 1
,• b = -14
,• c = 48
The next thing is to find ac
[tex]\begin{gathered} a\text{ = 1 and c = 48} \\ ac\text{ = 1 x 48} \\ ac\text{ = 48} \end{gathered}[/tex]Factors of 48: 1 and 48, 2 and 24, 4 and 12, 6 and 8, -1 and -48, -2 and -24, -4 and -12, -6 and -8
The next step is to find the factors of 48 that will give -14 when add and 48 when multiply together
The factors are -6 and -8
[tex]\begin{gathered} x^2\text{ -6x - 8x + 48 = 0} \\ x(x\text{ - 6) - 8(x - 6) = 0} \\ (x\text{ - 6) (x - 8) = 0} \\ (x\text{ - 6) = 0 or (x - 8) =0} \\ x\text{ - 6 = 0 or x - 8 = 0} \\ x\text{ = 0 + 6 or x = 0 + 8} \\ x\text{ = 6 or x = 8} \end{gathered}[/tex]Hence, the solution of the equation is x = 6 or x = 8
