Answer:
[tex]x=2+\frac{1}{2}\sqrt[]{21}[/tex]
or
[tex]x=2-\frac{1}{2}\sqrt{{21}[/tex]
Step-by-step explanation:
[tex]4x^2-16x-26=-21[/tex]
Add 21 on both sides.
[tex]4x^2-16x-26+21=-21+21[/tex]
[tex]4x^2-16x-5=0[/tex]
a=4
b=-16
c=-5
[tex]x=\frac{-b\frac{+}{}\sqrt[]{b^2-4ac} }{2a}[/tex]
[tex]x=\frac{-(-16)\frac{+}{}\sqrt[]{(-16)^2-4(4)(-5)} }{2(4)}[/tex]
[tex]x=\frac{16\frac{+}{}\sqrt[]{256+80} }{8}[/tex]
[tex]x=\frac{16\frac{+}{}\sqrt[]{336} }{8}[/tex]
[tex]x=\frac{16\frac{+}{}\sqrt[]{2^2*2^2*21} }{8}[/tex]
[tex]x=\frac{16\frac{+}{}2*2\sqrt[]{21} }{8}[/tex]
[tex]x=\frac{16\frac{+}{}4\sqrt[]{21} }{8}[/tex]
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[tex]x=\frac{16}{8}+\frac{4\sqrt[]{21}}{8}[/tex]
[tex]x=2+\frac{1}{2}\sqrt[]{21}[/tex]
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[tex]x=\frac{16}{8}-\frac{4\sqrt[]{21}}{8}\\x=2-\frac{1}{2}\sqrt{{21}[/tex]
