Problem 2
Question
Solve each equation in Exercises \(1-14\) by factoring. $$x^{2}-13 x+36=0$$
Step-by-Step Solution
Verified Answer
The solutions are \(x=4\) and \(x=9\).
1Step 1: Identifying the coefficients
Identify the values of \(a\), \(b\), and \(c\) in the equation \(ax^{2} + bx + c =0\). Here, \(a=1\), \(b=-13\), and \(c=36\).
2Step 2: Factoring the quadratic equation
Factor the quadratic equation. The factors of \(c\) such that their sum equals \(b\) are \( -4\) and \(-9\). When we consider these factors, the equation becomes \((x-4)(x-9)=0\).
3Step 3: Solving the factored equation
To solve for \(x\), set each factor equal to zero. This results in two equations, \(x-4=0\) and \(x-9=0\). Solving for \(x\) gives us the solutions \(x=4\) and \(x=9\).
Other exercises in this chapter
Problem 2
Plot the given point in a rectangular coordinate system. $$(2,5)$$
View solution Problem 2
Solve each polynomial equation in by factoring and then using the zero-product principle. $$ 5 x^{4}-20 x^{2}=0 $$
View solution Problem 2
In Exercises 1-12, graph the solutions of each inequality on a number line. $$x>-2$$
View solution Problem 2
In Exercises \(1-14\), let \(x\) represent the number. Write each English phrase as an algebraic expression. A number increased by 13
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