Using the quadratic formula, find the solution to 4x2+4x−15=0
.(1 point)
Responses
x=1.5
, x=−2.5
x equals 1.5 , x equals negative 2.5
x=−2.5
x equals negative 2.5
x=1.5
x equals 1.5
x=−1.5
, x=−2.5
x equals 1.5 , x equals negative 2.5
To find the solution to the quadratic equation 4x^2 + 4x - 15 = 0 using the quadratic formula, follow these steps:
1. Identify the coefficients: a = 4, b = 4, and c = -15.
2. Plug the values of a, b, and c into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, it becomes:
x = (-4 ± √(4^2 - 4(4)(-15))) / (2(4))
3. Simplify the expression inside the square root:
x = (-4 ± √(16 + 240)) / 8
x = (-4 ± √256) / 8
x = (-4 ± 16) / 8
4. Calculate the two possible solutions:
x1 = (-4 + 16) / 8 = 12 / 8 = 1.5
x2 = (-4 - 16) / 8 = -20 / 8 = -2.5
Therefore, the solutions to the equation 4x^2 + 4x - 15 = 0 using the quadratic formula are x = 1.5 and x = -2.5.
To find the solution to the equation 4x^2 + 4x - 15 = 0 using the quadratic formula, follow the steps below:
Step 1: Identify the coefficients a, b, and c from the equation. In this case, a = 4, b = 4, and c = -15.
Step 2: Substitute the values of a, b, and c into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values, we get:
x = (-4 ± √(4^2 - 4*4*(-15))) / (2*4)
Simplifying further:
x = (-4 ± √(16 + 240)) / 8
x = (-4 ± √(256)) / 8
Step 3: Simplify the equation inside the square root:
x = (-4 ± 16) / 8
Step 4: Further simplify the equation:
x = (-4 + 16) / 8 or x = (-4 - 16) / 8
x = 12 / 8 or x = -20 / 8
Simplifying further:
x = 3/2 or x = -5/2
Therefore, the solutions to the equation 4x^2 + 4x - 15 = 0 using the quadratic formula are:
x = 1.5 or x = -2.5