Question

Solve for x :-16x^2 + 60x + 1 = 0

Answer 1

x = -0.017 and x = 3.767

Step-by-step explanation

We are given the equation:

`-16x^2\text{ + 60x + 1 = 0 }`

Normally, we could have tried factorisation method, in which we would need two numbers that add up to 60 and their product is -16.

But we do not have such numbers, so we will use the Quadratic formula:

`x\text{ = }\frac{-b\text{ }\pm\sqrt[]{b^2\text{ - 4ac}}}{2a}`

The general form of a quadratic equation is:

`ax^2\text{ + bx + c = 0}`

So, comparing with the given equation, we have that:

a = -16, b = 60 and c = 1

Therefore:

`\begin{gathered} x\text{ = }\frac{-60\text{ }\pm\sqrt[]{60^2\text{ - (4 }\cdot\text{ -16 }\cdot\text{ 1)}}}{2\cdot\text{ -16}} \\ x\text{ = }\frac{-60\text{ }\pm\sqrt[]{3600\text{ - (-64)}}}{-32}\text{ = }\frac{-60\text{ }\pm\sqrt[]{3600\text{ + 64}}}{-32}\text{ = }\frac{-60\text{ }\pm\sqrt[]{3664}}{-32} \\ x\text{ = }(-60)/(-32)\text{ + }(60.53)/(-32)\text{ and x = }(-60)/(-32)\text{ - }(60.53)/(-32) \\ x\text{ = 1.875 - }1.892\text{ and x = 1.875 + 1.892} \\ x\text{ = -0.017 and x = 3.767} \end{gathered}`

That is the solution for the equation.