310=3x2−x

Question

310=3x2−x

Liyana Mansell · Accepted Answer

To solve 310=3x2−x, 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=3x2−x−310. 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 3x2−x−310, 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: 3x2−x−310=0 3x2−31x+30x−310=0  Rewrite the middle term. (3x2{2}−31x)+(30x−310)=0 Group each pair of terms. x(3x−31)+10(3x−31)=0  Factor out the GCF of each pair. (3x−31)(x+10)=0 Factor out 3x−31. 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 (3x−31)(x+10)=0, then 3x−31=0 or x+10=0. Solving each of these for x gives: 3x−31=0  x+10=0 3x=31  x=−10 x=313 ​ The solutions of the equation are then x=313 and x=−10

310=3x^{2}−x

Answered question

Answer & Explanation

New Questions in Algebra I