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 the equation for all real solutions in simplest form. -3r^(2)-r-10=-4r^(2)

Solve the equation for all real solutions in simplest form.\newline−3r2−r−10=−4r2 -3 r^{2}-r-10=-4 r^{2}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Simplify expressions using trigonometric identitiesright chevron icon

Full solution

Q. Solve the equation for all real solutions in simplest form.\newline−3r2−r−10=−4r2 -3 r^{2}-r-10=-4 r^{2}
  1. Move r2r^2 terms: Add 4r24r^2 to both sides of the equation to move all the r2r^2 terms to one side.\newline−3r2−r−10+4r2=−4r2+4r2-3r^2 - r - 10 + 4r^2 = -4r^2 + 4r^2\newlineThis simplifies to r2−r−10=0r^2 - r - 10 = 0.
  2. Factor quadratic equation: Factor the quadratic equation r2−r−10r^2 - r - 10. We look for two numbers that multiply to −10-10 and add to −1-1. These numbers are −5-5 and 22. So, the factored form is (r−5)(r+2)=0(r - 5)(r + 2) = 0.
  3. Solve for rr: Set each factor equal to zero and solve for rr.\newlineFirst, set r−5=0r - 5 = 0, which gives r=5r = 5.\newlineSecond, set r+2=0r + 2 = 0, which gives r=−2r = -2.

More problems from Simplify expressions using trigonometric identities

Question
If cos⁡(θ)=817 \cos(\theta)=\frac{8}{17} and 0∘<θ<90∘ 0^\circ<\theta<90^\circ , what is sec⁡(θ) \sec(\theta) ? Write your answer in simplified, rationalized form. sec⁡(θ)= \sec(\theta)= ______
Get tutor helpright-arrow

Posted 5 months ago

Question
cos⁡(x)=−0.3\cos(x) = -0.3. What is sin⁡(90∘−x)\sin(90^\circ - x)? ____
Get tutor helpright-arrow

Posted 8 months ago

Question
If csc⁡(θ)=178 \csc(\theta) = \frac{17}{8} and 0∘<θ<90∘ 0^\circ < \theta < 90^\circ , what is tan⁡(θ) \tan(\theta) ?\newlineWrite your answer in simplified, rationalized form.\newlinetan⁡(θ)= \tan(\theta) = ______\newline
Get tutor helpright-arrow

Posted 8 months ago

Question
Is the sine function even or odd?\newlineChoices:\newline[A]even\text{[A]even}\newline[B]odd\text{[B]odd}
Get tutor helpright-arrow

Posted 8 months ago

Question
Write the sentence as an equation. \newline8989 is equal to the quotient of yy and 1717 \newlineType a slash ( / / ) if you want to use a division sign. \newline_____
Get tutor helpright-arrow

Posted 7 months ago

Question
Write the sentence as an equation. \newline4545 is equal to the quotient of zz and 55 \newlineType a slash ( / / ) if you want to use a division sign. \newline_____
Get tutor helpright-arrow

Posted 9 months ago

Question
Solve for hh. \newline h2+24h=0h^2 + 24h = 0 \newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. \newline h=h = _____
Get tutor helpright-arrow

Posted 9 months ago

Question
h2−4h=0h^2 - 4h = 0
Get tutor helpright-arrow

Posted 7 months ago

Question
Combine the like terms to create an equivalent expression:\newline−k−(−8k)=□-k-(-8k)=\square
Get tutor helpright-arrow

Posted 10 months ago

Question
Which of the following degree measures is equal to 5π 5 \pi radians?\newline(The number of degrees of arc in a circle is 360360 . The number of radians of arc in a circle is 2π 2 \pi .)\newlineChoose 11 answer:\newline(A) 144∘ 144^{\circ} \newline(B) 900∘ 900^{\circ} \newline(C) 1,080∘ 1,080^{\circ} \newline(D) 1,800∘ 1,800^{\circ}
Get tutor helpright-arrow

Posted 7 months ago

View all (36)

Related topics

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