Using the formula method and the completing the square method solve solve
4x^2 - 5x - 8 = 0
To solve 4x^2 - 5x - 8 = 0 using the formula method, we will use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 4, b = -5, and c = -8.
x = (-(-5) ± √((-5)^2 - 4(4)(-8))) / (2(4))
x = (5 ± √(25 + 128)) / 8
x = (5 ± √(153)) / 8
Therefore, the solutions using the formula method are:
x = (5 + √153) / 8
x ≈ 2.28
x = (5 - √153) / 8
x ≈ -0.78
To solve 4x^2 - 5x - 8 = 0 using the completing the square method:
Step 1: Move the constant term (-8) to the right side of the equation.
4x^2 - 5x = 8
Step 2: Divide each term by the coefficient of x^2 (4).
x^2 - 5/4 x = 2
Step 3: Take half of the coefficient of x (-5/4) and square it.
(-5/4)^2 = 25/16
Step 4: Add the result from step 3 to both sides of the equation.
x^2 - 5/4 x + 25/16 = 2 + 25/16
x^2 - 5/4 x + 25/16 = 57/16
Step 5: Rewrite the left side of the equation as a perfect square trinomial.
(x - 5/4)^2 = 57/16
Step 6: Take the square root of both sides of the equation.
x - 5/4 = ±√(57/16)
Step 7: Solve for x.
x = 5/4 ±√(57/16)
Therefore, the solutions using the completing the square method are:
x ≈ 2.28
x ≈ -0.78