Quadratic Formula
1.)
[tex]y = \frac{ - 1}{2} + \frac{1}{2} \sqrt{3} [/tex]
Factoring Method
1.)
[tex] \frac{m = 3}{m = - 2} [/tex]
Step-by-step explanation:
Quadratic Formula
Step 1:
Simplify both sidra of the equation.
[tex]2y {}^{2} = - 2y + 1[/tex]
Step 2:
Subtract -2y+1 from both sidra.
[tex]2y {}^{2} - ( - 2y + 1) = - 2y + 1 - ( - 2y + 1)[/tex]
[tex]2y {}^{2} + 2y - 1 = 0[/tex]
For this equation: a = 2, b = 2.
c = -1
[tex]2y {}^{2} + 2y + - 1 = 0[/tex]
Step 3:
Use Quadratic Formula with a = 2, b = 2, c = -1.
[tex]y = \frac{ - b + - \sqrt{b {}^{2} - 4ac } }{2a} [/tex]
[tex]y = \frac{ - (2) + - \sqrt{(2) {}^{2} - 4(2)( - 1)} }{2(2)} [/tex]
[tex]y = \frac{ - 2 + - \sqrt{12} }{4} \\ y = \frac{ - 1 }{2} + \frac{1}{2} \sqrt{3} \: \: \: or \: \: y = \frac{ - 1}{2} + \frac{ - 1}{2} \sqrt{3} [/tex]
Factoring Method
Step 1:
Davide both sides by 2.
[tex]m {}^{2} - m - 6 = 0[/tex]
To Salve the equation, factor the left hand side by Groupon. First, left hand side needs to be rewritten as m² + am + be -6. To find a and b, set up a system to be solved.
[tex]a + b = - 1 \\ ab = 1( - 6) = - 6[/tex]
Since ab is negative, a and b have the opposite signs. Since a + b is negative, the negative number has greater absolute value than the positive. List all such integer para that give product –6.
[tex]1. - 6[/tex]
[tex]2. - 3[/tex]
Calculate the sum for each pair.
