Solve the equation 10w² + 1w - 3 = 0.

To solve the equation 10 w 2 + 1 w − 3 = 0 , we use the quadratic formula. The solutions are w = 2 1 ​ and w = − 5 3 ​ .
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Answered by Anonymous | 2025-07-04

To solve the quadratic equation 10 w 2 + 1 w − 3 = 0 , we can use the quadratic formula. The quadratic formula is given by:
w = 2 a − b ± b 2 − 4 a c ​ ​
where a , b , and c are the coefficients from the quadratic equation a x 2 + b x + c = 0 . In this equation, we have:

a = 10
b = 1
c = − 3

Now, we substitute these values into the quadratic formula:

First, calculate the discriminant b 2 − 4 a c : b 2 − 4 a c = 1 2 − 4 ( 10 ) ( − 3 ) = 1 + 120 = 121

Since the discriminant is positive, there are two real and distinct solutions. Calculate w :
w = 20 − 1 ± 121 ​ ​

Simplify the square root: 121 ​ = 11

Compute the solutions: w = 20 − 1 + 11 ​ = 20 10 ​ = 2 1 ​ w = 20 − 1 − 11 ​ = 20 − 12 ​ = − 5 3 ​


Therefore, the solutions to the equation are:
w = 2 1 ​ and w = − 5 3 ​

Answered by BenjaminOwenLewis | 2025-07-06