use the quadratic formula to solve the equation
4x^2-7x-2=0
Your equation is already in the form ax^2 + bx + c = 0
In your case,
a = 4, b = -7 and c = -2.
The quadratic formula for the solution values of x, which you should memorize or learn to derive, is
x = [-b +/- sqrt (b^2-4ac)]/2a
It would good practice for you to do the final alculation yourself
b^2-4ac = 81 in this case, and has a square root that is an integer, making the answer rather easy to write down.
x = -b/2a +/- (1/2a)sqrt(b^2 - 4 a c)
a = 4
b = -7
c = -2
x = 7/8 +/- (1/8) sqrt ( 49 + 32)
x = 7/8 +/- (1/8) sqrt (81)
lucky (9*9)=81
so
x = 7/8 +/- 9/8
x = 16/8 or -2/8 wow, nice polite numbers
so
x = 2 or - 1/4
To solve the quadratic equation 4x^2-7x-2=0 using the quadratic formula, follow these steps:
Step 1: Identify the coefficients of the equation. In this case, the coefficients are:
a = 4
b = -7
c = -2
Step 2: Plug the values of a, b, and c into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Step 3: Substitute the values of a, b, and c into the formula:
x = (7 ± √((-7)^2 - 4(4)(-2))) / 2(4)
Step 4: Simplify the expression inside the square root:
x = (7 ± √(49 + 32)) / 8
Step 5: Further simplify:
x = (7 ± √(81)) / 8
x = (7 ± 9) / 8
Step 6: Calculate both solutions by separating the positive and negative square root:
For the "+" solution:
x = (7 + 9) / 8
x = 16 / 8
x = 2
For the "-" solution:
x = (7 - 9) / 8
x = -2 / 8
x = -1/4
Therefore, the solutions to the equation 4x^2-7x-2=0 using the quadratic formula are:
x = 2 and x = -1/4.