Question
Solve and factor each equation
5x^2+16x=-3
5x^2+16x=-3
Answers
Answered by
GPT 3.5
To solve the equation 5x^2 + 16x = -3, we first need to set the equation to zero:
5x^2 + 16x + 3 = 0
Now, we need to factor the quadratic equation. Since this equation cannot be factored easily, you can use the quadratic formula to find the roots:
x = [-b ± √(b^2 - 4ac)] / 2a
For the given equation:
a = 5, b = 16, c = 3
Plugging these values into the formula, we get:
x = [-16 ± √(16^2 - 4*5*3)] / 2*5
x = [-16 ± √(256 - 60)] / 10
x = [-16 ± √196] / 10
x = (-16 ± 14) / 10
This gives us two roots:
x = (-16 + 14) / 10 = -2 / 10 = -0.2
x = (-16 - 14) / 10 = -30 / 10 = -3
Therefore, the roots of the equation 5x^2 + 16x + 3 = 0 are x = -0.2 and x = -3.
5x^2 + 16x + 3 = 0
Now, we need to factor the quadratic equation. Since this equation cannot be factored easily, you can use the quadratic formula to find the roots:
x = [-b ± √(b^2 - 4ac)] / 2a
For the given equation:
a = 5, b = 16, c = 3
Plugging these values into the formula, we get:
x = [-16 ± √(16^2 - 4*5*3)] / 2*5
x = [-16 ± √(256 - 60)] / 10
x = [-16 ± √196] / 10
x = (-16 ± 14) / 10
This gives us two roots:
x = (-16 + 14) / 10 = -2 / 10 = -0.2
x = (-16 - 14) / 10 = -30 / 10 = -3
Therefore, the roots of the equation 5x^2 + 16x + 3 = 0 are x = -0.2 and x = -3.