Write quadratic equation that can be solved by factoring. Solve your equation and show all your work.
Quadratic equation: x^2 - 5x + 6 = 0
To solve for x using factoring:
1. Find two numbers that multiply to 6 and add up to -5: -2 and -3
2. Rewrite the middle term using the two numbers: x^2 - 2x - 3x + 6 = 0
3. Factor by grouping: x(x - 2) - 3(x - 2) = 0
4. Factor out the common factor: (x - 2)(x - 3) = 0
5. Set each factor equal to zero and solve for x:
x - 2 = 0
x = 2
x - 3 = 0
x = 3
Therefore, the solutions to the quadratic equation x^2 - 5x + 6 = 0 are x = 2 and x = 3.
Do one with different numbers
Quadratic equation: x^2 + 7x + 12 = 0
To solve for x using factoring:
1. Find two numbers that multiply to 12 and add up to 7: 3 and 4
2. Rewrite the middle term using the two numbers: x^2 + 3x + 4x + 12 = 0
3. Factor by grouping: x(x + 3) + 4(x + 3) = 0
4. Factor out the common factor: (x + 3)(x + 4) = 0
5. Set each factor equal to zero and solve for x:
x + 3 = 0
x = -3
x + 4 = 0
x = -4
Therefore, the solutions to the quadratic equation x^2 + 7x + 12 = 0 are x = -3 and x = -4.