SOLUTION: Use the quadratic formula to solve: -x^2+7x-10=0

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Question 178400This question is from textbook
: Use the quadratic formula to solve: -x^2+7x-10=0 This question is from textbook

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%2B7x-10=0 Start with the given equation.


x%5E2-7x%2B10=0 Multiply EVERY term by -1 to make the leading coefficient positive.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-7, and c=10


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%2810%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-7, and c=10


x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%281%29%2810%29+%29%29%2F%282%281%29%29 Negate -7 to get 7.


x+=+%287+%2B-+sqrt%28+49-4%281%29%2810%29+%29%29%2F%282%281%29%29 Square -7 to get 49.


x+=+%287+%2B-+sqrt%28+49-40+%29%29%2F%282%281%29%29 Multiply 4%281%29%2810%29 to get 40


x+=+%287+%2B-+sqrt%28+9+%29%29%2F%282%281%29%29 Subtract 40 from 49 to get 9


x+=+%287+%2B-+sqrt%28+9+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%287+%2B-+3%29%2F%282%29 Take the square root of 9 to get 3.


x+=+%287+%2B+3%29%2F%282%29 or x+=+%287+-+3%29%2F%282%29 Break up the expression.


x+=+%2810%29%2F%282%29 or x+=++%284%29%2F%282%29 Combine like terms.


x+=+5 or x+=+2 Simplify.


So the answers are x+=+5 or x+=+2

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
-x%5E2+%2B+7x+-+10+=+0
When the equation is in the form
ax%5E2+%2B+bx+%2B+c+=+0, you can use the
quadratic formula which is:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+-1
b+=+7
c+=+-10
x+=+%28-7+%2B-+sqrt%28+7%5E2-4%2A%28-1%29%2A%28-10%29+%29%29%2F%282%2A%28-1%29%29+
x+=+%28-7+%2B-+sqrt%28+49+-+40+%29%29%2F%28-2%29+
x+=+%28-7+%2B-+sqrt%28+9+%29%29%2F%28-2%29+
The 2 answers are:
x+=+%287+-+3%29+%2F+2
x+=+2
and
x+=+%287+%2B+3%29+%2F+2
x+=+5
I can see directly that this is true, since
-x%5E2+%2B+7x+-+10+=+%28-x+%2B+5%29%28x+-+2%29
and
%28-x+%2B+5%29%28x+-+2%29+=+0
%28-5+%2B+5%29%285+-+2%29+=+0
0%2A3+=+0
0+=+0
%28-2+%2B+5%29%282+-+2%29+=+0
3%2A0+=+0
0+=+0