Solve b... I need step be step explanations
- Thread starter TinusB
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There are several ways we could approach this, but I think the simplest is to expand the left side, and then compare corresponding coefficients. You could also factor the RHS and compare factors. Can you do either of these?
pka
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\(\displaystyle \begin{align*}(x-b)(x-1)&=x^2+3x-4\\x^2+(b-1)x+b&=x^2+3x-4\\b-1&=3\\b&=4 \end{align*}\)
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If we expand the left side, we get:
[MATH]x^2-(b+1)x+b=x^2+3x-4[/MATH]
Looking at the constant terms (those without \(x\) we then see that we must have:
[MATH]b=-4[/MATH]
If we look at the linear terms, equating coefficients, we get:
[MATH]b+1=-3[/MATH]
[MATH]b=-4[/MATH]
If we factor the right side of the original equation, we get:
[MATH](x-b)(x-1)=(x+4)(x-1)[/MATH]
This implies:
[MATH]b=-4[/MATH]
Does this make sense?
No, Denis, you corrected the left-hand side, but then you mishandled it after that.
Then x(-b - 1) = 3x -->
-b - 1 = 3 -->
-b = 4 -->
b = -4 . . . . . . . . . . . . . . . This is the desired variable and the value.
Damn it....that was a typo; should be:
left side should be: x^2 + x(-b-1), which results in x = -4
Truly having a bad day...thanks Lookagain...
Otis
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We use the caret symbol ^ to show exponents:
(x - b)(x - 1) = x^2 + 3x - 4
When an exponent contains more than a single value, then type grouping symbols around it:
f(t) = a*e^(-kt)
PS: There's a link in the forum's submission guidelines to a page that shows how to type math expressions using a keyboard.
?
Steven G
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As MarkFL said you could factor the rhs and get (x-1)(x+4) and this must equal (x-b)(x-1) so (x+4) = (x-b). Subtract x from both sides (unless you already see the answer!) and get 4=-x or x=-4.