3x²+8x=35
it needs to be a factored answer thanks
3x²+8x=35
3x^2 + 8x -35 = 0
Find two factors of the end terms that will add to the middle term.
(3x-7)(x+5) = 0
X = -5, 7/3
To solve the quadratic equation 3x² + 8x = 35, we need to rearrange the equation to bring it into the standard quadratic form: ax² + bx + c = 0. In this case, the equation is already in this form.
Now, we can solve the equation through factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula, which is often the easiest method in this case.
The quadratic formula states that for any quadratic equation in the form ax² + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b² - 4ac)) / (2a)
In our equation, a = 3, b = 8, and c = -35, so we can substitute these values into the quadratic formula:
x = (-8 ± √(8² - 4 * 3 * -35)) / (2 * 3)
Simplifying this equation further, we have:
x = (-8 ± √(64 + 420)) / 6
x = (-8 ± √484) / 6
x = (-8 ± 22) / 6
Now, we can calculate the two possible values of x:
x₁ = (-8 + 22) / 6 = 14 / 6 = 7/3
x₂ = (-8 - 22) / 6 = -30 / 6 = -5
Therefore, the solutions to the equation 3x² + 8x = 35 are x = 7/3 and x = -5.