2x2 + 6x - 3 = 5

Question

2x² + 6x - 3 = 5

Answer 1

I'm assuming you need to solve for x:

2x² + 6x - 3 = 5.

So, 2x² + 6x - 8 = 0. (subtract 5 from both sides)

Then 2(x² + 3x - 4) = 0, (factor out a 2 from each term)

And x² + 3x - 4 = 0. (divide by 2 on each side)

To factor this quadratic, we need factors that multiply to give -4 and add to give +3, namely +4 and -1.

So (x + 4) (x - 1) = 0 and x = -4 or +1.

 

Check: 2(-4)² + 6(-4) - 3 = 2(16) -24 -3 = 5

and 2(1)² + 6(1) - 3 = 2(1) + 6 - 3 = 5.

Answer 2

2x^2+6x-3=5 which implies by the subtraction property of equality that we will get 2x^2+6x-3-5=5-5 which further implies by the additive inverse property that we will get 2x^2+6x-3-5=0 which by simplifying we will get that 2x^2+6x-8=0 which further implies by factoring the greatest common factor of 2,6, and 8 is 2 and so this will simplify to 2(x^2+3x-4)=0 which further implies by using the division property of equality we will get that this will turn out to be 2/2(x^2+3x-4)=0/2 which further implies by the multiplicative inverse property that we will get 1/1(x^2+3x-4)=0/2 which will simplify to 1(x^2+3x-4)=0 which further implies by the identity property of multiplication that we will get x^2+3x-4=0 which makes this a quadratic equation or quadratic polynomial equation in which we can use trial and error, ac method, completing the square, or the quadratic formula. Now since it is faster and easier for convention I am going to use trial and error so I am going to look for two factor that its product is -4 and its sum is 3 so in this case it is +4 and -1 and for x^2 we will factor it into x and x since x*x=x^2 by the exponential law a^m*a^n=a^m+n and so with that said we will get (x+4)(x-1)=0 which further implies by the zero factor principle that we will get that (x+4)=0 or(x-1)=0 and so for x+4=0 we will subtract 4 from both sides of the equality using the subtraction property of equality and get x+4-4=0-4 and then I will use the additive inverse property to arrive x+0=0-4 and then conclude by using the identity property of addition that x=-4 and now in a similar manner I am going to do for x-1=0 so first I am going to add 1 to both sides of the equality by utilizing the addition property of equality in which implies that we will get x-1+1=0+1 which further implies by the additive inverse property that we will get x+0=0+1 which hence give us x=1 by the identity property of addition and so with that said our solutions for this quadratic equation will be x=-4 or x=1 and with that said we are done. If you wish to check the answers all you do is substitute the results individually for x in the original quadratic equation. For instance for the first I will substitute 1 to get 2(1)^2+6(1)-3=5 which is exactly what the right hand side of the equation is and so the left hand side of the equation equals to the right hand side of the equation and so that is a solution and you will do the same for -4 and that concludes the lesson for now. Hope to hear back from you with soon with comments on my solution.