Answer:
[tex]x = 8\±\sqrt{10[/tex]
[tex]a =8[/tex] [tex]b = 10[/tex]
Step-by-step explanation:
Given
[tex]x^2 - 16x + 54 = 0[/tex]
Required
Complete the square
[tex]x^2 - 16x + 54 = 0[/tex]
Subtract 54 from both sides
[tex]x^2 - 16x + 54 -54= 0-54[/tex]
[tex]x^2 - 16x = -54[/tex]
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Take half of - 16
[tex](-16/2) = -8[/tex]
Square the result
[tex](-8)^2 = 64[/tex]
Add the squared result to both sides of the equation
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So, we have:
[tex]x^2 - 16x +64= -54+64[/tex]
[tex]x^2 - 16x +64= 10[/tex]
Expand
[tex]x^2 - 8x - 8x + 64 = 10[/tex]
Factorize
[tex]x(x - 8) - 8(x - 8) = 10[/tex]
Factor out x - 8
[tex](x - 8)(x - 8) = 10[/tex]
[tex](x - 8)^2 = 10[/tex]
Take square roots
[tex]x - 8 = \±\sqrt{10[/tex]
Solve for x
[tex]x = 8\±\sqrt{10[/tex]
We have:
[tex]x = a - \sqrt{b}[/tex]
[tex]x = a + \sqrt{b}[/tex]
By comparing the above with: [tex]x = 8\±\sqrt{10[/tex]
