52-x2+x=10

Question

52-x²+x=10

x=

Answer 1

When you check highest power of 'x', it is 2 then it is quadratic equation of the form ax^_²+bx+c=0  we can solve equation to get thevalue of 'x' obviously we get 2 values for x.

we can do factorization or we can use the formula

52-x²+x=10 is -x²+x+42=0

Multiply on both sides with -1 thenthe equation becomes x²-x-42=0

x²-7x+6x-42=0

x(x-7)+6(x-7)=0

(x-7)(x+6)=0

x=7 and x=-6

If the factorization does not work then we apply quadratic method where we can find the value of

x=(-b± √b²-4ac) /2a.

 

Answer 2

Hi, Mart.

This equation has an x² in it, so it is a quadratic equation. If we move the terms around to the standard form, it would be: (Note that I subtracted the 10 to set the equation equal to zero).

-x² + x + 42 = 0

There are 3 ways to solve this kind of  quadratic equation: factoring, completing the square, and the quadratic formula.

Since you didn't specify that you had to use a certain method, I am going to factor it. Since the first term is -x², the factors have to start with x and -x.

(-x     )(x      ) = 0

Since the 3rd term is positive, both signs will be the same. Since the middle term is also positive, both signs would be positive.

(x +    )(-x +   ) = 0

Remember we now have to find a pair of factors for the 3rd term that add or subtract to the coefficient of the 2nd. That is, a pair of factors of 42 that add or subtract to 1.
42 = 7 * 6, and 7 - 6 = 1, so now put 6 and 7 into the equation so that it works out correctly:

(x + 6)(-x + 7) = 0

Since the factors multiply to zero, one of the factors has to be equal to zero:

x + 6 = 0           or           -x + 7 = 0

Solving these gives you x = -6 or x = 7.

Hope this helps!

Answer 3

Hello Mart,

It is a quadratic equation, therefore x will have two answers.

First bring the equation in quadratic form which is ax² + bx + c = 0.

52 - x² + x = 10

subtract 10 from both sides so we can get rid of 10 on right hand side.

52 - x² + x - 10 = 10 - 10

42 - x² + x = 0

now rearrange

-x² + x + 42 = 0

multiply the whole equation by -1 to make x² term positive

-1(-x² + x + 42) = -1(0)

distribute -1

x² - x - 42 = 0 (quadratic equation in the form ax² + bx + c = 0)

Now factors of 42 are +6 and -7 which when multiplied gives -42 (c term) and when added gives -1(b term). Therefore, factorize the quadratic equation given.

x² + 6x - 7x - 42 = 0

use the grouping method to factorize it.

x(x + 6) -7(x + 6) = 0

(x + 6) (x - 7) = 0

To make the equation zero either x + 6 = 0 or x - 7 = 0

Therfore on solving you'll get x = -6 and x = +7 (answers)

I hope this helps you.