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

类似问题

What are the roots of 𝑓 ( 𝑡 ) = − 𝑡 2 + 7 𝑡 − 10 ?

If 𝑥 2 = 49 , which of the following gives the value(s) of 𝑥 ?

What are the roots of the expression 𝑥 2 + 5 𝑥 = 0 ?

What are the roots of the expression 𝑥 2 − 7 𝑥 + 6 = 0 ?

Part 1Solve by using the square root property.(xminus−77)squared2equals=6464 Part 1The solution(s) is(are) x = [input]enter your response here .(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)

Part 1Solve the given quadratic equation by factoring.63 x minus 36 x squared equals 063x−36x2=0 Part 1xequals=[input]00 (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

Part 1Solve the given quadratic equation by factoring.63 x minus 36 x squared equals 063x−36x2=0 Part 1xequals=[input]enter your response here (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单