Quadratic Equations Online Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
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Question
Use factoring to find the solutions for 30=−x2+13x
.(1 point)
Responses

x=3,10
x equals 3 comma 10

x=−10,−3
x equals negative 10 comma negative 3

x=−10,3
x equals negative 10 comma 3

x=−3,10
x equals negative 3 comma 10
Remaining Attempts : 3
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Answer 1

To solve the equation \(30 = -x^2 + 13x\) using factoring, we first rearrange the equation into standard quadratic form:

1. Move all terms to one side of the equation: \[ -x^2 + 13x - 30 = 0 \]

2. Multiply through by -1 to make the coefficient of \(x^2\) positive: \[ x^2 - 13x + 30 = 0 \]

3. Now, we need to factor the quadratic. We look for two numbers that multiply to \(30\) (the constant term) and add to \(-13\) (the coefficient of the \(x\) term). The numbers that fit this criteria are \(-3\) and \(-10\).

4. We can express the quadratic as: \[ (x - 3)(x - 10) = 0 \]

5. Setting each factor equal to zero gives us the solutions: \[ x - 3 = 0 \quad \Rightarrow \quad x = 3 \] \[ x - 10 = 0 \quad \Rightarrow \quad x = 10 \]

Thus, the solutions are: \[ x = 3, \quad x = 10 \]

So the correct response is: x=3,10