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Solve the quadratic equation using the completing the square method

x^2 = 40 - 6x

User Zhang Buzz
by
8.3k points

2 Answers

6 votes

Answer: x=4 or x=-10

Step-by-step explain: Factoring x2+6x-40

The first term is, x2 its coefficient is 1 .

The middle term is, +6x its coefficient is 6 .

The last term, "the constant", is -40

Step-1 : Multiply the coefficient of the first term by the constant 1 • -40 = -40

Step-2 : Find two factors of -40 whose sum equals the coefficient of the middle term, which is 6 .

-40 + 1 = -39

-20 + 2 = -18

-10 + 4 = -6

-8 + 5 = -3

-5 + 8 = 3

-4 + 10 = 6 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 10

x2 - 4x + 10x - 40

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-4)

Add up the last 2 terms, pulling out common factors :

10 • (x-4)

Step-5 : Add up the four terms of step 4 :

(x+10) • (x-4)

Which is the desired factorization

User Daniel Eagle
by
8.7k points
2 votes

Answer:

x=4,-10

Explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

User XeniaSis
by
8.1k points

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