Question

question 7(3 points) solve by factoring: 2x² - 11x = 40 (put answers in order from least to greatest) the factors are(2x + )(x + )=0 which means x= or x= blank 1: blank 2: blank 3: blanks

Explanation:

Step1: Rearrange the equation

First, rewrite \(2x^{2}-11x = 40\) as \(2x^{2}-11x - 40=0\).

Step2: Factor the quadratic equation

We need to find two numbers \(a\) and \(b\) such that \(a\times b=2\times(- 40)=-80\) and \(a + b=-11\). The numbers are \(a = -16\) and \(b = 5\).
Then, \(2x^{2}-16x+5x - 40 = 0\).
Group the terms: \(2x(x - 8)+5(x - 8)=0\).
Factor out \((x - 8)\): \((2x + 5)(x-8)=0\).

Step3: Solve for \(x\)

Set each factor equal to zero.
For \(2x+5 = 0\), we have \(2x=-5\), so \(x=-\frac{5}{2}\).
For \(x - 8=0\), we have \(x = 8\).

Answer:

Blank 1: \(5\)
Blank 2: \(-8\)
Blank 3: \(-\frac{5}{2}\)
Blank 4: \(8\)