Solution of Quadratic Equation (Math Problem Sample)

Solution of x2-2x-15=0
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Solution
Method 1
Solve by factoring method
x2-2x-15=0
Find the product and the sum of the equation
Product=1×-15=-15 and sum=-2
Expand the equation
x2-5x+3x-15=0
Factorise
x+3x-5=0
Set each equation equal to zero
x+3=0 or x-5=0
x=-3 or 5
Method 2
Solve by Quadratic method
ax2+bx+c=0
x=-b±b2-4ac2a
x2-2x-15=0
Apply the quadratic formula
x=2±(-2)2-(4)(1)(-15)2(1)
x=2±4+602
x=2±642
Simplify the equation
x=2±82
x=2+82 or2-82=0
x=102 or-62=0
x=5 or-3
Method 3
Completing Square method
Put the equation in the form of ax2+bx=-c
x2-2x=15
Make sure a=1
Using the value of b from new equation, addb22 to both sides of the equation to form a perfect square on the left side of the equation
c=-222=1
x2-2x+1=15+1
x2-2x+1=16
Find the square root on both sides
x-1=±4
Solve the result of the equation
x=4+1 or-4+1
x=5 or-3