# Solution of Quadratic Equation (Math Problem Sample)

Solve for x in the equation below using three different methods

x^2-2x-15=0

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

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