solve m2+6m+7 using completing the square method
poorly worded question.
We only "solve" equations, you don't have an equation.
I will assume you meant:
m^2 + 6m + 7 = 0
m^2 + 6m + .... = -7 + .....
m^2 + 6m + 9 = -7 + 9
(m+3)^2 = 2
m+3 = ± √2
m = -3 ± √2
answer
To solve the quadratic equation m^2 + 6m + 7 using the completing the square method, follow these steps:
Step 1: Begin with the quadratic equation in the form ax^2 + bx + c = 0. In this case, a = 1, b = 6, and c = 7.
Step 2: Divide the coefficient of the x-term by 2 and square the result. In this case, (6/2)^2 = 9.
Step 3: Add the squared result from step 2 to both sides of the equation. m^2 + 6m + 7 + 9 = 9
Simplifying the equation gives m^2 + 6m + 16 = 0.
Step 4: Rewrite the left side of the equation as a perfect square trinomial. To do this, take half of the coefficient of the middle term (6/2 = 3), square it (3^2 = 9), and add it to both sides of the equation.
m^2 + 6m + 9 = -7
Step 5: Rewrite the left side of the equation as a perfect square trinomial – (m + p)^2 = q.
(m + 3)^2 = -7
Step 6: Take the square root of both sides of the equation.
m + 3 = ±√(-7)
Step 7: Solve for m by subtracting 3 from both sides of the equation.
m = -3 ±√(-7)
Since the square root of a negative number is not a real number, the quadratic equation m^2 + 6m + 7 has no real solutions.