Question

question
use the quadratic formula to solve. express your answer in simplest form.
( d^2 + 10d + 28 = 3 )
answer
attempt 1 out of 4
additional solution no solution
( d = )
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Explanation:

Step1: Rewrite the equation in standard form

First, we need to rewrite the equation \(d^{2}+10d + 28=3\) in the standard quadratic form \(ax^{2}+bx + c = 0\). Subtract 3 from both sides:
\(d^{2}+10d+28 - 3=0\)
\(d^{2}+10d + 25=0\)
Here, \(a = 1\), \(b = 10\), and \(c = 25\).

Step2: Apply the quadratic formula

The quadratic formula is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\). For our equation, \(x = d\), so we substitute the values of \(a\), \(b\), and \(c\) into the formula:
First, calculate the discriminant \(\Delta=b^{2}-4ac\). Substitute \(a = 1\), \(b = 10\), \(c = 25\):
\(\Delta=(10)^{2}-4\times1\times25\)
\(=100 - 100\)
\(=0\)
Then, substitute into the quadratic formula:
\(d=\frac{-10\pm\sqrt{0}}{2\times1}\)
\(=\frac{-10\pm0}{2}\)

Step3: Simplify the expression

Since \(\pm0\) doesn't change the value, we have:
\(d=\frac{-10}{2}=- 5\)

Answer:

\(d=-5\)