SOLUTION: Can somebody please help me? 2. What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation "12x2 - 10x - 42 = 0".

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Question 154171This question is from textbook elementary and intermediate algebra concepts and applications
: Can somebody please help me?
2. What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation "12x2 - 10x - 42 = 0".
This question is from textbook elementary and intermediate algebra concepts and applications

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You can solve by 1) factoring, 2) quadratic formula, and 3) completing the square. I'll do the second technique to get you started




12x%5E2-10x-42=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=12, b=-10, and c=-42


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2-4%2812%29%28-42%29+%29%29%2F%282%2812%29%29 Plug in a=12, b=-10, and c=-42


x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%2812%29%28-42%29+%29%29%2F%282%2812%29%29 Negate -10 to get 10.


x+=+%2810+%2B-+sqrt%28+100-4%2812%29%28-42%29+%29%29%2F%282%2812%29%29 Square -10 to get 100.


x+=+%2810+%2B-+sqrt%28+100--2016+%29%29%2F%282%2812%29%29 Multiply 4%2812%29%28-42%29 to get -2016


x+=+%2810+%2B-+sqrt%28+100%2B2016+%29%29%2F%282%2812%29%29 Rewrite sqrt%28100--2016%29 as sqrt%28100%2B2016%29


x+=+%2810+%2B-+sqrt%28+2116+%29%29%2F%282%2812%29%29 Add 100 to 2016 to get 2116


x+=+%2810+%2B-+sqrt%28+2116+%29%29%2F%2824%29 Multiply 2 and 12 to get 24.


x+=+%2810+%2B-+46%29%2F%2824%29 Take the square root of 2116 to get 46.


x+=+%2810+%2B+46%29%2F%2824%29 or x+=+%2810+-+46%29%2F%2824%29 Break up the expression.


x+=+%2856%29%2F%2824%29 or x+=++%28-36%29%2F%2824%29 Combine like terms.


x+=+7%2F3 or x+=+-3%2F2 Simplify.


So the answers are x+=+7%2F3 or x+=+-3%2F2