Solve 3x^2+19x-14=0 using the quadratic formula
I will be happy to check your work.
x = [ - 19 �} �ã (361 + 168) ] / 6
x = [ - 19 �} �ã (529) ] / 6
x = [ - 19 �} 23 ] / 6
x = 4 / 6 , x = - 42 / 6
x = 2/3 , x = - 7
To solve the quadratic equation 3x^2 + 19x - 14 = 0 using the quadratic formula, we can follow these steps:
Step 1: Identify the coefficients
From the given equation, we can identify the coefficients:
a = 3
b = 19
c = -14
Step 2: Write down the quadratic formula
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac))/(2a)
Step 3: Substitute the coefficients into the formula
Substitute the coefficients a = 3, b = 19, and c = -14 into the quadratic formula:
x = (-19 ± √(19^2 - 4 * 3 * -14))/(2 * 3)
Step 4: Simplify the equation
Now, let's simplify the equation:
x = (-19 ± √(361 + 168))/(6)
x = (-19 ± √(529))/(6)
x = (-19 ± 23)/(6)
Step 5: Calculate both solutions
Now, calculate both solutions for x by considering both the positive and negative values after the ±:
x1 = (-19 + 23)/(6)
x1 = 4/6
x1 = 2/3
x2 = (-19 - 23)/(6)
x2 = -42/6
x2 = -7
So, the solutions to the quadratic equation 3x^2 + 19x - 14 = 0 are x = 2/3 and x = -7.