Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for nn.\newlinen2+13n+22=0n^2 + 13n + 22 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. \newlineIf there are multiple solutions, separate them with commas.\newlinen=n = ____

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Solve a quadratic equation by factoringright chevron icon

Full solution

Q. Solve for nn.\newlinen2+13n+22=0n^2 + 13n + 22 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. \newlineIf there are multiple solutions, separate them with commas.\newlinen=n = ____
  1. Identify quadratic equation: Identify the quadratic equation to be solved.\newlineThe given quadratic equation is n2+13n+22=0n^2 + 13n + 22 = 0. We need to find two numbers that multiply to 2222 and add up to 1313.
  2. Factor quadratic equation: Factor the quadratic equation.\newlineWe are looking for two numbers that multiply to give 2222 and add to give 1313. The numbers 1111 and 22 satisfy these conditions because 11×2=2211 \times 2 = 22 and 11+2=1311 + 2 = 13.\newlineSo, we can write the quadratic equation as (n+11)(n+2)=0(n + 11)(n + 2) = 0.
  3. Solve using zero product property: Solve for nn using the zero product property.\newlineIf (n+11)(n+2)=0(n + 11)(n + 2) = 0, then either n+11=0n + 11 = 0 or n+2=0n + 2 = 0.
  4. Solve first equation: Solve the first equation n+11=0n + 11 = 0.\newlineSubtract 1111 from both sides to isolate nn.\newlinen+11−11=0−11n + 11 - 11 = 0 - 11\newlinen=−11n = -11
  5. Solve second equation: Solve the second equation n+2=0n + 2 = 0. Subtract 22 from both sides to isolate nn. n+2−2=0−2n + 2 - 2 = 0 - 2 n=−2n = -2

More problems from Solve a quadratic equation by factoring

Question
Solve for v v .\newlinev2+8v+12=0 v^2+8v+12=0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinev= v=_____
Get tutor helpright-arrow

Posted 3 months ago

Question
Solve for u u .\newlineu2=9 u^2 = 9 \newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlineu= u = _____ or u= u = _____
Get tutor helpright-arrow

Posted 8 months ago

Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinek2−20k+_____k^2 - 20k + \_\_\_\_\_
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve by completing the square.\newlineu2−24u−23=0u^2 - 24u - 23 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`u` = ________ or `u` =______
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the discriminant. \newline2q2−9q+8=02q^2 - 9q + 8 = 0\newline______
Get tutor helpright-arrow

Posted 4 months ago

Question
Solve the system of equations.\newliney=22x−38 y = 22x - 38 \newliney=x2+11x−14 y = x^2 + 11x - 14 \newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(_,_) (\_,\_) \newline(_,_) (\_,\_)
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve for aa.\newline(a+5)(a+1)=0(a + 5)(a + 1) = 0\newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlinea=a = _____ or a=a = _____
Get tutor helpright-arrow

Posted 8 months ago

Question
Let p=x2−7 p=x^{2}-7 . Which equation is equivalent to (x2−7)2−4x2+28=5 (x^{2}-7)^{2}-4x^{2}+28=5 in terms of p p ? Choose 11 answer: \newline(A) p2−4p+23=0 p^{2}-4p+23=0 \newline(B) p2+4p−5=0 p^{2}+4p-5=0 \newline(C) p2−4p−5=0 p^{2}-4p-5=0 \newline(D) p2+4p+23=0 p^{2}+4p+23=0
Get tutor helpright-arrow

Posted 8 months ago

Question
Let m=2x+3m=2x+3. Which equation is equivalent to (2x+3)2−14x−21=−6(2x+3)^{2}-14x-21=-6 in terms of mm? Choose 11 answer: \newline(A) m2+7m+6=0m^{2}+7m+6=0 \newline(B) m2−7m−15=0m^{2}-7m-15=0 \newline(C) m2−7m+6=0m^{2}-7m+6=0 \newline(D) m2+7m−15=0m^{2}+7m-15=0
Get tutor helpright-arrow

Posted 8 months ago

Question
Let m=x2+3m=x^{2}+3. Which equation is equivalent to (x2+3)2+7x2+21=−10(x^{2}+3)^{2}+7x^{2}+21=-10 in terms of mm? Choose 11 answer:\newline(A) m2−7m+31=0m^{2}-7m+31=0\newline(B) m2+7m+31=0m^{2}+7m+31=0\newline(C) m2−7m+10=0m^{2}-7m+10=0\newline(D) m2+7m+10=0m^{2}+7m+10=0
Get tutor helpright-arrow

Posted 9 months ago

View all (122)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant