Hi there! We can create a number equation to find your solution. Already, we know that two consecutive integers can be represented by [tex]x+x+1[/tex]. All we have to do is square that expression and make it equal to 452. This gives us:
[tex](x)^{2} +(x+1)^{2} =452[/tex]
We can simplify that down to [tex]2x^{2}+4x+4 =452[/tex]. Now, we can subtract 452 from both sides to make the whole left side equation equal to zero. Doing that gives us [tex]2x^{2}+4x-448=0[/tex]. We see that 2 can be factored out of the whole equation, giving us [tex] 2(x^{2}+2x-224)=0[/tex]. Next, we can factor the equation to get [tex](x-16)(x+14)=0[/tex]. We can use the Zero Product Property to find the x values of -16 and 14. Therefore, the two integers are -16 and 14. Hope this helped!
