Step 1. Write your equation in standard form.
5x^2 + 2x -3 = 05x2+2x−3=0
Step 2. Move the constant to the right hand side of the equation.
Add 33 to each side .
5x^2+2x -3 +3 = 0+35x2+2x−3+3=0+3
5x^2+2x = 35x2+2x=3
Step 3. Divide both sides of the equation by the coefficient of x^2x2.
Divide both sides by 5.
x^2 +2/5x =3/5x2+25x=35
Step 4. Square the coefficient of x and divide by 4.
(2/5)^2/4 = (4/25)/4 = 1/25(25)24=4254=125
Step 5. Add the result to each side.
x^2 +2/5x + 1/25 =3/5 + 1/25x2+25x+125=35+125
x^2 +2/5x + 1/25= 15/25 + 1/25x2+25x+125=1525+125
x^2 +2/5x + 1/25 =16/25x2+25x+125=1625
Step 6. Take the square root of each side.
x+1/5 = ±4/5 x+15=±45
Case 1
x_1 + 1/5 = +4/5x1+15=+45
x_1 = 4/5-1/5 = (4-1)/5x1=45−15=4−15
x_1 = 3/5x1=35
Case 2
x_2 + 1/5 = -4/5x2+15=−45
x_2 = -4/5-1/5 = (-4-1)/5 = (-5)/5x2=−45−15=−4−15=−55
x_2 = -1x2=−1
So x = 3/5x=35 or x = -1x=−1
Check: Substitute the values of xx back into the quadratic.
(a) x = 3/5x=35
5x^2 + 2x -3 = 5(3/5)^2 + 2(3/5) -3 = 5(9/25) + 6/5 -3 = 9/5 +6/5 -15/5 = (9+6-15)/5 = 05x2+2x−3=5(35)2+2(35)−3=5(925)+65−3=95+65−155=9+6−155=0.
(b) x = -1x=−1
5x^2 + 2x -3 = 5(-1)^2 + 2(-1) -3 = 5(1) – 2 -3 = 5-2-3 = 0
