2p^2 + 8p = -3
Answer is p = -4 + or - square root of 10
over 2
Answer is p = -4 + or - square root of 10
over 2
To solve the equation 2p^2 + 8p = -3, we can use the quadratic formula. The quadratic formula states that for an equation in the form of ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 2, b = 8, and c = -3. Plugging these values into the quadratic formula, we get:
p = (-8 ± √(8^2 - 4(2)(-3))) / (2(2))
Simplifying further:
p = (-8 ± √(64 + 24)) / 4
p = (-8 ± √88) / 4
p = (-8 ± √(4 * 22)) / 4
p = (-8 ± 2√22) / 4
Now we can simplify the expression by factoring out a 2:
p = 2(-4 ± √22) / 4
Cancelling out the 2 and 4:
p = -4 ± √22 / 2
Therefore, the solutions to the equation 2p^2 + 8p = -3 are:
p = (-4 + √22) / 2
p = (-4 - √22) / 2
These can be further simplified to:
p = -4 + √22 / 2
p = -4 - √22 / 2
So the answer is p = -4 + or - square root of 22 over 2.