SOLUTION: what is the solution set of the equation x^2-7x =-6

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Question 550663: what is the solution set of the equation x^2-7x =-6
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-7x=-6 Start with the given equation.


x%5E2-7x%2B6=0 Add 6 to both sides.


Notice that the quadratic x%5E2-7x%2B6 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-7, and C=6


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-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%281%29%286%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-7, and C=6


x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%281%29%286%29+%29%29%2F%282%281%29%29 Negate -7 to get 7.


x+=+%287+%2B-+sqrt%28+49-4%281%29%286%29+%29%29%2F%282%281%29%29 Square -7 to get 49.


x+=+%287+%2B-+sqrt%28+49-24+%29%29%2F%282%281%29%29 Multiply 4%281%29%286%29 to get 24


x+=+%287+%2B-+sqrt%28+25+%29%29%2F%282%281%29%29 Subtract 24 from 49 to get 25


x+=+%287+%2B-+sqrt%28+25+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%287+%2B-+5%29%2F%282%29 Take the square root of 25 to get 5.


x+=+%287+%2B+5%29%2F%282%29 or x+=+%287+-+5%29%2F%282%29 Break up the expression.


x+=+%2812%29%2F%282%29 or x+=++%282%29%2F%282%29 Combine like terms.


x+=+6 or x+=+1 Simplify.


So the solutions are x+=+6 or x+=+1

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E2+-+7x+=+-6+
Complete the square
+x%5E2+-+7x+%2B+%287%2F2%29%5E2+=+-6+%2B+%287%2F2%29%5E2+
+x%5E2+-+7x+%2B+49%2F4+=+-24%2F4+%2B+49%2F4+
+%28+x+-+7%2F2+%29%5E2+=+25%2F4+
take the square root of both sides
+x+-+7%2F2+=+5%2F2+
+x+=+12%2F2+
+x+=+6+
and, taking the negative square root,
+x+-+7%2F2+=+-5%2F2+
+x+=+2%2F2+
+x+=+1+
The solution set is (6,0) and (1,0)
check:
+%28+x+-+6+%29%2A%28+x+-+1+%29+=+0+
+%28+x+-+6+%29%2A%28+x+-+1+%29+=+x%5E2+-+7x+%2B+6+
+x%5E2+-+7x+%2B+6+=+0+
+x%5E2+-+7x+=+-6+
OK