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Alessandro wrote the quadratic equation [tex]\(-6 = x^2 + 4x - 1\)[/tex] in standard form. What is the value of [tex]\(c\)[/tex] in his new equation?

A. [tex]\(c = -6\)[/tex]
B. [tex]\(c = -1\)[/tex]
C. [tex]\(c = 5\)[/tex]
D. [tex]\(c = 7\)[/tex]

Sagot :

GinnyAnswer
To determine the value of [tex]\( c \)[/tex] in the standard form of Alessandro's quadratic equation, we need to follow several steps.

First, let's start with the given equation:
[tex]\[ -6 = x^2 + 4x - 1 \][/tex]

We need to rewrite this equation into the standard form of a quadratic equation, which is typically:
[tex]\[ ax^2 + bx + c = 0 \][/tex]

To do this, we'll move all the terms to one side of the equation so that it equals zero. Let's first add 6 to both sides of the given equation:
[tex]\[ x^2 + 4x - 1 + 6 = 0 \][/tex]

Next, combine the constant terms on the left side:
[tex]\[ x^2 + 4x + 5 = 0 \][/tex]

Now we have the quadratic equation in standard form:
[tex]\[ x^2 + 4x + 5 = 0 \][/tex]

In this standard form, [tex]\( c \)[/tex] is the constant term. Comparing the resulting equation with the standard form [tex]\( ax^2 + bx + c = 0 \)[/tex], we see that:

[tex]\[ c = 5 \][/tex]

Thus, the value of [tex]\( c \)[/tex] in Alessandro's new equation is:
[tex]\[ c = 5 \][/tex]

So, the correct answer is:
[tex]\[ c = 5 \][/tex]
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