Solve using C.T.S.M
2m rase to power 2 +5m-20=0
To solve the quadratic equation 2m^2 + 5m - 20 = 0 using the C.T.S.M (Completing the Square Method), follow these steps:
Step 1: Make sure the equation is in the standard form of a quadratic equation - ax^2 + bx + c = 0. In this case, 2m^2 + 5m - 20 is already in standard form.
Step 2: Identify the values of a, b, and c. In this equation, a = 2, b = 5, and c = -20.
Step 3: Write the equation in a new form, completing the square for the quadratic term. To do this, take half of the coefficient of the linear term (b) and square it. Add this value to both sides of the equation.
Begin by evaluating (b/2)^2: (5/2)^2 = 6.25
Rewrite the equation: 2m^2 + 5m + 6.25 - 6.25 - 20 = 0
Step 4: Simplify the equation:
2m^2 + 5m + 6.25 - 26.25 = 0
2m^2 + 5m - 20 = 0
Step 5: Group the terms:
(2m^2 + 5m + 6.25) - 26.25 = 0
Step 6: Recognize the perfect square trinomial in the parentheses.
Notice that (2m^2 + 5m + 6.25) can be factored into (m + 2.5)^2.
Step 7: Rewrite the equation with the perfect square trinomial:
(m + 2.5)^2 - 26.25 = 0
Step 8: Isolate the perfect square term by adding 26.25 to both sides of the equation:
(m + 2.5)^2 = 26.25
Step 9: Take the square root of both sides of the equation:
m + 2.5 = ±√(26.25)
Step 10: Solve for m by isolating m on one side:
m = -2.5 ± √(26.25)
Thus, the solutions to the equation 2m^2 + 5m - 20 = 0 using the C.T.S.M are m = -2.5 + √(26.25) and m = -2.5 - √(26.25).