Solve for the roots in simplest form using the quadratic formula:4x^2 +53= −28x
To solve for the roots using the quadratic formula, we need to first rewrite the equation in the standard form of a quadratic equation: ax^2 + bx + c = 0
Given equation: 4x^2 + 28x + 53 = 0
Now, we can apply the quadratic formula:
x = [-b ± √(b^2 - 4ac)] / 2a
In this case, a = 4, b = 28, and c = 53
Plugging these values into the quadratic formula:
x = [-28 ± √(28^2 - 4 * 4 * 53)] / 2 * 4
x = [-28 ± √(784 - 848)] / 8
x = [-28 ± √(-64)] / 8
x = [-28 ± 8i] / 8
x = -3.5 ± i
Therefore, the roots of the given equation in simplest form are: -3.5 ± i