Solve the quadratic by factoring:

x2−14x+3=−5(x+3)

If you have multiple answers, separate them with a comma. Reduce all fractions. Enter fractions using "/".

Question

Solve the quadratic by factoring:

x2−14x+3=−5(x+3)

If you have multiple answers, separate them with a comma.   Reduce all fractions.  Enter fractions using "/".

BlackTom AI · Accepted Answer

First, restate the problem in my own words to ensure understanding: Solve the quadratic equation given by x^2 − 14x + 3 = −5(x + 3) by factoring, and if there are multiple answers, list them separated by a comma and in reduced fraction form if needed.

Step 1: Bring all terms to one side to set the equation to zero. Starting from x^2 − 14x + 3 = −5(x + 3), distribute the on the right: −5(x + 3) = −5x − 15. Then add 5x + 15 to both sides to collect like terms: x^2 − 14x + 3 + 5x + 15 = 0, which simplifies to x^2 − 9x + 18 = 0.

Step 2: Factor the quadratic x^2 − 9x + 18. Look for two numbers that multiply to 18 and add to −9. The pair −3 and −6 works because (−3)(−6) = 18 and (−3) + (−6) = −9. Therefore, x^2 − 9x + 18 factors as (x − 3)(x − 6).

Step 3: Solve the factored form. Set each factor equal to zero: x − 3 = 0 or x − 6 = 0. This yields x = 3 or x = 6.

Step 4: Consider the required output format. The problem asks to enter multiple answers separated by a comma and to reduce fractions if any. Here we have two integer solutions, so the valid outputs are “3,6” or “6,3” depending on the desired order. Since no ordering constraint is specified, both orders are correct, and either can be accepted.

Note on precision: No fractions appear in the final solution, so there is no need for fraction formatting beyond standard integer literals.

If you’re checking work: substitute x = 3 into the original equation: left side 3^2 − 14·3 + 3 = 9 − 42 + 3 = −30, right side −5(3 + 3) = −5·6 = −30, equal. For x = 6: left side 36 − 84 + 3 = −45, right side −5(9) = −45, equal as well. This confirms both solutions are valid.

Solve the quadratic by factoring: x2−14x+3=−5(x+3) If you have multiple answers, separate them with a comma. Reduce all fractions. Enter fractions using "/".简答题

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