Question 268742: How do you solve 5x^2-9x+1=x^2-14x+7?
Answer by persian52(161)   (Show Source):
You can put this solution on YOUR website! 5x^(2)-9x+1=x^(2)-14x+7
Move all terms not containing x to the right-hand side of the equation.
5x^(2)-9x+1-x^(2)+14x=7
Since 5x^(2) and -x^(2) are like terms, add -x^(2) to 5x^(2) to get 4x^(2).
4x^(2)-9x+1+14x=7
Since -9x and 14x are like terms, subtract 14x from -9x to get 5x.
4x^(2)+5x+1=7
To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.
4x^(2)+5x-6=0
Find the factors such that the product of the factors is the trinomial 4x^(2)+5x-6. This can be done by trial and error and checked using the FOIL method of simplifying polynomials.
(x+2)(4x-3)=0
Set each of the factors of the left-hand side of the equation equal to 0.
x+2=0_4x-3=0
Since 2 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2 from both sides.
x=-2_4x-3=0
Set each of the factors of the left-hand side of the equation equal to 0.
x=-2_4x-3=0
Since -3 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 3 to both sides.
x=-2_4x=3
Divide each term in the equation by 4.
x=-2_(4x)/(4)=(3)/(4)
Simplify the left-hand side of the equation by canceling the common terms.
x=-2_x=(3)/(4)
The complete solution is the set of the individual solutions.
x=-2,(3)/(4)
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