X^2-15x+10=0

To solve the quadratic equation x^2 - 15x + 10 = 0, you can use the quadratic formula or factorization method.

Method 1: Using the quadratic formula The quadratic formula is given by x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 1, b = -15, and c = 10. Plugging these values into the quadratic formula, we have:

x = (-(-15) ± √((-15)^2 - 4(1)(10))) / (2(1)) x = (15 ± √(225 - 40)) / 2 x = (15 ± √185) / 2

So the solutions are: x1 = (15 + √185) / 2 x2 = (15 - √185) / 2

Method 2: Using factorization To use the factorization method, we need to find two numbers whose product is equal to 10 and whose sum is equal to -15. In this case, the numbers are -5 and -2.

Rewriting the quadratic equation in factored form, we have: (x - 5)(x - 2) = 0

Setting each factor equal to zero, we get: x - 5 = 0 or x - 2 = 0

Solving these equations, we have: x = 5 or x = 2

So the solutions are: x1 = 5 x2 = 2

Therefore, the solutions to the quadratic equation x^2 - 15x + 10 = 0 are x1 = 5, x2 = 2, x3 = (15 + √185) / 2, and x4 = (15 - √185) / 2.