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 x. Enter the solutions from least to greatest. {:[3x^(2)+3x-90=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newline3x2+3x−90=0 lesser x=□ greater x=□ \begin{array}{l} 3 x^{2}+3 x-90=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}

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 x x . Enter the solutions from least to greatest.\newline3x2+3x−90=0 lesser x=□ greater x=□ \begin{array}{l} 3 x^{2}+3 x-90=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
  1. Write Equation: Write down the given quadratic equation.\newline3x2+3x−90=03x^2 + 3x - 90 = 0\newlineWe need to solve for xx.
  2. Factor GCF: Factor out the greatest common factor (GCF) if possible.\newlineThe GCF of the coefficients 3x23x^2, 3x3x, and −90-90 is 33. Let's factor it out.\newline3(x2+x−30)=03(x^2 + x - 30) = 0
  3. Factor Quadratic Expression: Now we need to factor the quadratic expression x2+x−30x^2 + x - 30.\newlineWe are looking for two numbers that multiply to −30-30 and add up to 11 (the coefficient of xx).\newlineThe numbers 66 and −5-5 work because 6×(−5)=−306 \times (-5) = -30 and 6+(−5)=16 + (-5) = 1.\newlineSo we can write the factored form as:\newline3(x+6)(x−5)=03(x + 6)(x - 5) = 0
  4. Solve for x (Part 11): Set each factor equal to zero and solve for x.\newlineFirst, we set the factor x+6x + 6 equal to zero:\newlinex+6=0x + 6 = 0\newlineSubtract 66 from both sides:\newlinex=−6x = -6
  5. Solve for x (Part 22): Set the other factor x−5x - 5 equal to zero:\newlinex−5=0x - 5 = 0\newlineAdd 55 to both sides:\newlinex=5x = 5
  6. Write Solutions: Write down the solutions in ascending order.\newlineThe lesser value of xx is −6-6, and the greater value of xx is 55.

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