how do I solve for 16x^2+56x-120
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quadratic equation online
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16x^2+56x-120=0
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I assume you meant
solve 16x^2+56x-120=0 , you must have an "equation" to solve for it.
divide by 8
2x^2 + 7x - 15 = 0
(2x-3)(x+5) = 0
x = 3/2 or x = -5
To solve the quadratic equation 16x^2 + 56x - 120, you can use factoring or the quadratic formula.
1. Factoring Method:
First, check if there is a common factor among the terms. In this case, all coefficients are divisible by 8, so we can factor out 8:
8(2x^2 + 7x - 15)
Then, try to further factorize the quadratic term inside the parentheses. The equation can be factored as follows:
8(2x - 3)(x + 5)
Set each factor equal to zero and solve for x:
2x - 3 = 0 or x + 5 = 0
Solving these two equations gives you the following solutions:
2x = 3 or x = -5
x = 3/2 or x = -5
Therefore, the solutions to the equation 16x^2 + 56x - 120 are x = 3/2 and x = -5.
2. Quadratic Formula:
The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
For the equation 16x^2 + 56x - 120, the values of a, b, and c are:
a = 16, b = 56, c = -120
Substituting these values into the quadratic formula, we get:
x = (-56 ± sqrt(56^2 - 4*16*(-120))) / (2*16)
x = (-56 ± sqrt(3136 + 7680)) / 32
x = (-56 ± sqrt(10816)) / 32
x = (-56 ± 104) / 32
Solving these two equations gives you the following solutions:
x = (-56 + 104) / 32 or x = (-56 - 104) / 32
x = 48/32 or x = -160/32
x = 3/2 or x = -5
Therefore, the solutions to the equation 16x^2 + 56x - 120 are x = 3/2 and x = -5.
Both methods should yield the same solutions, which are x = 3/2 and x = -5.