Question

Yea solve equation by factoring
7x² - 39x + 17 = -3

Answer 1

Answer:

x = 4/7, 5

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Answer 2

Answer:

x = 4/7 or x = 5

Step-by-step explanation:

Step 1: Add to 3 to both sides

• $7x^2-39x+17+3=-3+3$
• $7x^2-39x+20=0$

Step 2: Factor by grouping

This equation is in the form ax² + bx + c = 0. Since there are no terms that multiply to 20 and add to -39, we have to find terms that multiply to a (7) * (20) and add to -39.

• Factors of 140: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140
• -35 x -4 = 120, and -35 - 4 = -39. Thus, the two terms are -35 and -4.

Now, we split -39x into -35x and -4.

• 7x^2 - 35x - 4x + 20.
• (7x² - 35x) + (-4x + 20)

Next, we factor each expression in the parentheses. After that, we put the terms outside the parentheses together. Reminder, the terms inside the parentheses should be the same.

• $7x(x-5)-4(x-5)$
• $(7x-4)(x-5) = 0$

Step 3: Solve for x using 7x - 4 = 0 and x - 5 = 0.

• $7x-4=0$
• $7x-4+4=0+4$
• $7x=4$
• $7x/7 = 4/7$
• $x= 4/7$

or

• $x-5=0$
• $x-5+5=0+5$
• $x=5$