SOLUTION: Solve for x: 3x^2+5x-7=x^2+8x+28
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Question 120219
:
Solve for x: 3x^2+5x-7=x^2+8x+28
Answer by
jim_thompson5910(35256)
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Start with the given equation
Subtract x^2 from both sides. Subtract 8x from both sides. Subtract 28 from both sides.
Combine like terms
Let's use the quadratic formula to solve for x:
Starting with the general quadratic
the general solution using the quadratic equation is:
So lets solve
( notice
,
, and
)
Plug in a=2, b=-3, and c=-35
Negate -3 to get 3
Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because
.)
Multiply
to get
Combine like terms in the radicand (everything under the square root)
Simplify the square root (note: If you need help with simplifying the square root, check out this
solver
)
Multiply 2 and 2 to get 4
So now the expression breaks down into two parts
or
Lets look at the first part:
Add the terms in the numerator
Divide
So one answer is
Now lets look at the second part:
Subtract the terms in the numerator
Divide
So another answer is
So our solutions are:
or