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Answer: x = 5, x = -7/2
<u>Step-by-step explanation:</u>
2x² - 3x - 35 = 0
<u>Step 1:</u> Find two values whose product = 2(-35) and sum = -3: -10 & 7
<u>Step 2: </u>Replace the b-value of -3x with -10x + 7x:
2x² - 10x + 7x - 35 = 0
<u>Step 3:</u> Factor the first two terms and the second two terms:
2x(x - 5) +7(x - 5) = 0
<u>Step 4</u>: Write the factored form:
Notice that the parenthesis are identical. This is one of the factors. The outside values are the other factor:
Parenthesis: (x - 5)
Outside: (2x + 7)
Factored form: (x - 5)(2x + 7) = 0
<u>Step 5: </u>Set each factor each to zero and solve for x:
x - 5 = 0 2x + 7 = 0
x - 5