310=3x^{2}−x

glasskerfu 2021-01-31 Answered
310=3x2x
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Expert Answer

Liyana Mansell
Answered 2021-02-01 Author has 97 answers

To solve 310=3x2x, we first need to move all the terms to one side to write the equation in standard form. Subtracting 310 on both sides then gives 0=3x2x310.
To factor a quadratic of the form ax2+bx+c, you need to find two numbers, m and n, such that mn=ac and m+n=b. You can then rewrite the middle term as bx=mx+nx and factor by grouping.
For 3x2x310, a=3, b=−1, and  c=310 so mn=ac=3(310)=930 and m+n=b=1. Therefore m=31 and n=30 since (31)(30)=930 and 31+30=1. You can then rewrite the middle term as x=31x+30x and then factor by grouping:
3x2x310=0
3x231x+30x310=0  Rewrite the middle term.
(3x2{2}31x)+(30x310)=0 Group each pair of terms.
x(3x31)+10(3x31)=0  Factor out the GCF of each pair.
(3x31)(x+10)=0 Factor out 3x31.
Now that we have the equation factored, we can use the Zero Product Property to solve for x. The Zero Product Property states that if ab=0, then a=0 or b=0. Therefore, if (3x31)(x+10)=0, then 3x31=0 or x+10=0. Solving each of these for x gives:
3x31=0

x+10=0
3x=31

x=10
x=313
The solutions of the equation are then x=313 and x=10

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