Solve 9x² +14x-8=0
by completing the square
method.
Answers
Answer:
(x) = 9x² + 14x - 8
By completing the square method:
\mathsf {x^2 + \frac{14}{9}x - \frac{8}{9} = 0 }x
2
+
9
14
x−
9
8
=0
\mathsf {(x + \frac{14}{18})^2 - (\frac{14}{18})^2 - \frac{8}{9} = 0}(x+
18
14
)
2
−(
18
14
)
2
−
9
8
=0
\mathsf {(x + \frac{14}{18})^2 - (\frac{14}{18})^2 - \frac{8}{9} = 0}(x+
18
14
)
2
−(
18
14
)
2
−
9
8
=0
\mathsf {(x + \frac{14}{18})^2 - \frac{196}{324} - \frac{8}{9} = 0}(x+
18
14
)
2
−
324
196
−
9
8
=0
\mathsf {(x + \frac{14}{18})^2 - (\frac{196 + 288}{324}) = 0}(x+
18
14
)
2
−(
324
196+288
)=0
\mathsf {(x + \frac{14}{18})^2 - \frac{484}{324} = 0}(x+
18
14
)
2
−
324
484
=0
\mathsf {(x + \frac{14}{18})^2 = \frac{484}{324}}(x+
18
14
)
2
=
324
484
\mathsf {x + \frac{14}{18} = ± \sqrt{\frac{484}{324}}}x+
18
14
=±
324
484
\mathsf {x + \frac{14}{18} = ± \frac{22}{18}}x+
18
14
=±
18
22
\mathsf {x = \frac{-14}{18} ± \frac{22}{18}}x=
18
−14
±
18
22
\mathsf {x = \frac{-14}{18} + \frac{22}{18} \:\:\:\:\:\:OR\:\:\:\:\frac{-14}{18} - \frac{22}{18}}x=
18
−14
+
18
22
OR
18
−14
−
18
22
\mathsf {x = \frac{8}{18} \:\:\:\:\:\:OR\:\:\:\:\: \frac{-36}{18}}x=
18
8
OR
18
−36