SOLUTION: Find the solution the following quadratic equation X^2-12x+144=0 X^2+3x-28=0

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Question 1091043: Find the solution the following quadratic equation
X^2-12x+144=0
X^2+3x-28=0
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The standard form of a quadratic function is ax%5E2%2Bbx%2Bc=0 where
ax%5E2 is the quadratic term
bx is the linear term
c is the constant term
discriminant b%5E2-4ac tells us how many and what kind of roots quadratic function have
if b%5E2-4ac%3E0 quadratic function have two real roots
if b%5E2-4ac=0 quadratic function have one double root
if b%5E2-4ac%3C0 quadratic function have two complex roots

let check discriminant in your case
x%5E2-12x%2B144=0...... b%5E2-4ac->%28-12%29%5E2-4%2A1%2A144->144-576->-432%3C0; so, your quadratic function will have have two complex roots
use quadratic formula to find roots:
1.
x%5E2-12x%2B144=0
x+=+%28-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%2A1%2A144+%29%29%2F%282%2A1%29+
x+=+%2812+%2B-+sqrt%28+-432+%29%29%2F2+
x+=+%2812+%2B-+i%2Asqrt%28+432+%29%29%2F2+
x+=+%2812+%2B-+i%2A12+sqrt%283%29%29%2F2+
x+=+%28cross%2812%296+%2B-+i%2Across%2812%296+sqrt%283%29%29%2Fcross%282%29+
x+=+6+%2B+6i%2Asqrt%283%29
x+=+6+-+6i%2Asqrt%283%29

+graph%28+600%2C+600%2C+-10%2C+200%2C+-10%2C+200%2C+x%5E2-12x%2B144%29+


2.
x%5E2%2B3x-28=0
let check discriminant in this case:
b%5E2-4ac->3%5E2-4%2A1%2A%28-28%29->9%2B112->121%3E0; so, your quadratic function will have have two real roots

x%5E2%2B3x-28=0....factor completely
x%5E2%2B7x-4x-28=0
%28x%5E2%2B7x%29-%284x%2B28%29=0
x%28x%2B7%29-4%28x%2B7%29=0
%28x+-+4%29+%28x+%2B+7%29+=+0
solutions:
if %28x+-+4%29++=+0-> x=4
if +%28x+%2B+7%29+=+0-> x=-7
+graph%28+600%2C+600%2C+-30%2C+30%2C+-30%2C+30%2C+x%5E2%2B3x-28%29+


Answer by ikleyn(52876) About Me  (Show Source):
You can put this solution on YOUR website!
.
On solving quadratic equations, see the lessons
    - Introduction into Quadratic Equations
    - PROOF of quadratic formula by completing the square
    - HOW TO solve quadratic equation by completing the square - Learning by examples
in this site.


Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Quadratic equations".