Answer:
1.
[tex](2x-5)^2-54=0\\[/tex]
[tex]4x^2-20x+25-54=0[/tex]
[tex]4x^2-20x-29=0[/tex]
a = 4
b = -20
c = -29
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(-20)\pm\sqrt{(-20)^2-4(4)(-29)}}{2(4)}\\\\[/tex]
[tex]x=\frac{5+3\sqrt{6}}{2}[/tex]
[tex]x=\frac{5-3\sqrt{6}}{2}[/tex]
2.
[tex]4(3x-2)^2-11=1[/tex]
[tex]4(9x^2-12x+4)-11=1[/tex]
[tex]36x^2-48x+16-11-1=0[/tex]
[tex]36x^2-48x+4=0[/tex]
a = 36
b = -48
c = 4
[tex]x=\frac{-(-48)\pm\sqrt{(-48)^2-4(36)(4)}}{2(36)}[/tex]
[tex]x=\frac{2+\sqrt{3}}{3}[/tex]
[tex]x=\frac{2-\sqrt{3}}{3}[/tex]
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Verified answer
Answer:
1.
[tex](2x-5)^2-54=0\\[/tex]
[tex]4x^2-20x+25-54=0[/tex]
[tex]4x^2-20x-29=0[/tex]
a = 4
b = -20
c = -29
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(-20)\pm\sqrt{(-20)^2-4(4)(-29)}}{2(4)}\\\\[/tex]
[tex]x=\frac{5+3\sqrt{6}}{2}[/tex]
[tex]x=\frac{5-3\sqrt{6}}{2}[/tex]
2.
[tex]4(3x-2)^2-11=1[/tex]
[tex]4(9x^2-12x+4)-11=1[/tex]
[tex]36x^2-48x+16-11-1=0[/tex]
[tex]36x^2-48x+4=0[/tex]
a = 36
b = -48
c = 4
[tex]x=\frac{-(-48)\pm\sqrt{(-48)^2-4(36)(4)}}{2(36)}[/tex]
[tex]x=\frac{2+\sqrt{3}}{3}[/tex]
[tex]x=\frac{2-\sqrt{3}}{3}[/tex]