Suppose you are a solving a quadratic equation using the quadratic formula and this is your work so far:
2x^2+7x-15=0
AAAaannndd the bot gets it wrong yet again!
(-7 - 13) / 4 = -5
not -5/2 !!
I apologize for the mistake. Yes, you are correct that (-7 - 13) / 4 = -5. Therefore, the solutions to the quadratic equation 2x^2+7x-15=0 are x=3/2 and x=-5. Thank you for pointing that out.
To solve the quadratic equation 2x^2 + 7x - 15 = 0 using the quadratic formula, follow these steps:
Step 1: Identify the coefficients of the equation.
In this case,
a = 2
b = 7
c = -15
Step 2: Substitute the values of a, b, and c into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Applying the values from the equation:
x = (-7 ± √(7^2 - 4 * 2 * -15)) / (2 * 2)
Step 3: Simplify the expression inside the square root:
x = (-7 ± √(49 + 120)) / 4
x = (-7 ± √169) / 4
x = (-7 ± 13) / 4
Step 4: Solve for both possible values of x:
a) x = (-7 + 13) / 4
x = 6 / 4
x = 3/2
Therefore, one solution is x = 3/2.
b) x = (-7 - 13) / 4
x = -20 / 4
x = -5
Therefore, the other solution is x = -5.
So, the solutions to the quadratic equation 2x^2 + 7x - 15 = 0 are x = 3/2 and x = -5.
The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / 2a
In this equation, a = 2, b = 7, and c = -15.
Substituting these values into the formula, we get:
x = (-7 ± √(7^2 - 4(2)(-15))) / (2)(2)
Simplifying inside the square root:
x = (-7 ± √(169)) / 4
x = (-7 ± 13) / 4
This gives us two possible solutions:
x = (-7 + 13) / 4 = 3/2
x = (-7 - 13) / 4 = -5/2
Therefore, the solutions to the quadratic equation 2x^2+7x-15=0 are x=3/2 and x=-5/2.