Question

For what value of m is the equation true?
x^{2} +10x+11= m+(x=5)^2-25

Answer 1

The value of m that makes the equation x^2 + 10x + 11 equal to m + (x + 5)^2 - 25 is 11.

Step-by-step explanation:

The student is asking for the value of m that would make the equation x^2 + 10x + 11 equal to m + (x + 5)^2 - 25. First, let's simplify the right side of the equation by expanding (x + 5)^2:

(x + 5)^2 = x^2 + 2 × 5 × x + 52 = x^2 + 10x + 25.

Now plug this back into the original equation:

x^2 + 10x + 11 = m + (x^2 + 10x + 25) - 25

Combining like terms leaves us with the original left-side expression:

x^2 + 10x + 11 = m + x^2 + 10x

To find the value of m that satisfies the equation, we set equal the terms that don't contain x:

11 = m

So, the value of m for which the equation is true is 11.

Answer 2

We are given the equation:

x^2 + 10x + 11 = m + (x-5)^2 - 25

To determine the value of m, assign a value of x and solve for m

if x = 1, the equation becomes

1^2 + 10(1) + 11 = m + (1 -5)^2 - 25

solve for m

m = 31

When m = 31, the equation is true.