Question
Solving Quadratic Equations Using Patterns Practice
Supply the numbers to write x2+10x=16=0 in its factored form. Enter the lesser number first.
(x+_)(x+_)=0
Supply the numbers to write x2+10x=16=0 in its factored form. Enter the lesser number first.
(x+_)(x+_)=0
Answers
GPT-4o mini
To solve the equation \(x^2 + 10x - 16 = 0\) using factoring, we first rewrite the quadratic equation in the standard form.
The equation is already in standard form:
\[ x^2 + 10x - 16 = 0. \]
Next, we need to factor it. We are looking for two numbers that multiply to \(-16\) (the constant term) and add up to \(10\) (the coefficient of the linear term).
The two numbers that satisfy this condition are \(12\) and \(-2\), since:
\[ 12 \times (-2) = -24, \]
and
\[ 12 + (-2) = 10. \]
Thus, we can rewrite the equation as:
\[ (x + 12)(x - 2) = 0. \]
Putting it in the requested form, we should enter:
\[
(x + (-2))(x + 12) = 0.
\]
So the final answer is:
\[
(x - 2)(x + 12) = 0.
\]
Thus, the numbers to fill in the blanks are:
\(-2\) and \(12\).
So, your answer is:
\((x - 2)(x + 12) = 0.\)
The equation is already in standard form:
\[ x^2 + 10x - 16 = 0. \]
Next, we need to factor it. We are looking for two numbers that multiply to \(-16\) (the constant term) and add up to \(10\) (the coefficient of the linear term).
The two numbers that satisfy this condition are \(12\) and \(-2\), since:
\[ 12 \times (-2) = -24, \]
and
\[ 12 + (-2) = 10. \]
Thus, we can rewrite the equation as:
\[ (x + 12)(x - 2) = 0. \]
Putting it in the requested form, we should enter:
\[
(x + (-2))(x + 12) = 0.
\]
So the final answer is:
\[
(x - 2)(x + 12) = 0.
\]
Thus, the numbers to fill in the blanks are:
\(-2\) and \(12\).
So, your answer is:
\((x - 2)(x + 12) = 0.\)