Quadratic formula
x^2+6x+8-0 (solve by factoring)
(second Problem)
5w^2-3=0
Please show steps
x^2+6x+8 = 0
(x+2)(x+4) = 0
Since (x+a)(x+b) = x^2 + (a+b)x + ab
you are looking for factors of 8 that add up to 6.
5w^2-3 = 0
5w^2 = 3
w^2 = 3/5
w = ±√(3/5)
To solve the equation x^2 + 6x + 8 = 0 by factoring, follow these steps:
Step 1: Write down the equation:
x^2 + 6x + 8 = 0
Step 2: Look for two numbers that multiply to give you the constant term (in this case, 8) and add up to give you the coefficient of the x term (in this case, 6). The numbers that satisfy this condition are 2 and 4 since 2 * 4 = 8 and 2 + 4 = 6.
Step 3: Rewrite the middle term using these two numbers:
x^2 + 2x + 4x + 8 = 0
Step 4: Group the terms:
(x^2 + 2x) + (4x + 8) = 0
Step 5: Factor out the greatest common factor from each grouping:
x(x + 2) + 4(x + 2) = 0
Step 6: Combine like terms:
(x + 2)(x + 4) = 0
Step 7: Set each factor equal to zero and solve for x:
x + 2 = 0 --> x = -2
or
x + 4 = 0 --> x = -4
Hence, the solutions to the equation x^2 + 6x + 8 = 0 are x = -2 and x = -4.
Now let's solve the equation 5w^2 - 3 = 0 using the quadratic formula:
Step 1: Write down the equation:
5w^2 - 3 = 0
Step 2: Identify the coefficients:
a = 5, b = 0, c = -3
Step 3: Write down the quadratic formula:
w = (-b ± √(b^2 - 4ac)) / (2a)
Step 4: Plug in the values:
w = (-(0) ± √((0)^2 - 4(5)(-3))) / (2(5))
Step 5: Simplify:
w = (± √(0 + 60)) / 10
w = (± √60) / 10
Step 6: Simplify the square root:
w = (± √(4 * 15)) / 10
w = (± 2√15) / 10
Step 7: Further simplify:
w = (± √15) / 5
So the solutions to the equation 5w^2 - 3 = 0 are w = (√15) / 5 and w = -(√15) / 5.