Answer :
Sure! Let's solve the equation step by step.
We are given the equation:
[tex]\[ 4x^2 = 76 \][/tex]
Our goal is to identify the 'c' value in this equation. To do that, we need to rewrite the equation in the standard form of a quadratic equation, which is:
[tex]\[ ax^2 + bx + c = 0 \][/tex]
1. First, we need to bring all terms to one side of the equation so that the equation is set to 0. We do this by subtracting 76 from both sides:
[tex]\[ 4x^2 - 76 = 0 \][/tex]
2. Now, our equation is in the standard form [tex]\(ax^2 + bx + c = 0\)[/tex]. Here:
- [tex]\(a\)[/tex] is the coefficient of [tex]\(x^2\)[/tex] (which is 4),
- [tex]\(b\)[/tex] is the coefficient of [tex]\(x\)[/tex] (which is 0, since there is no [tex]\(x\)[/tex] term),
- [tex]\(c\)[/tex] is the constant term.
3. Looking at the equation [tex]\(4x^2 - 76 = 0\)[/tex]:
- The [tex]\(c\)[/tex] value is the constant term, which is [tex]\(-76\)[/tex].
So, the 'c' value is:
[tex]\[ \boxed{-76} \][/tex]
The correct option is:
[tex]\[ \mathbf{D) \, -76} \][/tex]
We are given the equation:
[tex]\[ 4x^2 = 76 \][/tex]
Our goal is to identify the 'c' value in this equation. To do that, we need to rewrite the equation in the standard form of a quadratic equation, which is:
[tex]\[ ax^2 + bx + c = 0 \][/tex]
1. First, we need to bring all terms to one side of the equation so that the equation is set to 0. We do this by subtracting 76 from both sides:
[tex]\[ 4x^2 - 76 = 0 \][/tex]
2. Now, our equation is in the standard form [tex]\(ax^2 + bx + c = 0\)[/tex]. Here:
- [tex]\(a\)[/tex] is the coefficient of [tex]\(x^2\)[/tex] (which is 4),
- [tex]\(b\)[/tex] is the coefficient of [tex]\(x\)[/tex] (which is 0, since there is no [tex]\(x\)[/tex] term),
- [tex]\(c\)[/tex] is the constant term.
3. Looking at the equation [tex]\(4x^2 - 76 = 0\)[/tex]:
- The [tex]\(c\)[/tex] value is the constant term, which is [tex]\(-76\)[/tex].
So, the 'c' value is:
[tex]\[ \boxed{-76} \][/tex]
The correct option is:
[tex]\[ \mathbf{D) \, -76} \][/tex]
