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 using the quadratic formula.\newlinej2−5j+1=0j^2 - 5j + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinej=j = _____ or j=j = _____

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Solve a quadratic equation using the quadratic formularight chevron icon

Full solution

Q. Solve using the quadratic formula.\newlinej2−5j+1=0j^2 - 5j + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinej=j = _____ or j=j = _____
  1. Quadratic Formula Definition: The quadratic formula is given by j=−b±b2−4ac2aj = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients from the quadratic equation in the form aj2+bj+c=0aj^2 + bj + c = 0. For our equation, a=1a = 1, b=−5b = -5, and c=1c = 1.
  2. Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. For our equation, this is (−5)2−4(1)(1)=25−4=21(-5)^2 - 4(1)(1) = 25 - 4 = 21.
  3. Apply Quadratic Formula: Now, apply the quadratic formula with the values of aa, bb, and cc. We have j=−(−5)±212×1=5±212j = \frac{-(-5) \pm \sqrt{21}}{2 \times 1} = \frac{5 \pm \sqrt{21}}{2}.
  4. Simplify Solutions: Since 21\sqrt{21} cannot be simplified into a perfect square, we will leave it as is under the square root. The two solutions for jj are j=5+212j = \frac{5 + \sqrt{21}}{2} and j=5−212j = \frac{5 - \sqrt{21}}{2}.
  5. Calculate Decimal Approximations: To express the solutions as decimals rounded to the nearest hundredth, we calculate each one. For j=5+212j = \frac{5 + \sqrt{21}}{2}, the approximate value is 5+4.582≈9.582≈4.79\frac{5 + 4.58}{2} \approx \frac{9.58}{2} \approx 4.79. For j=5−212j = \frac{5 - \sqrt{21}}{2}, the approximate value is 5−4.582≈0.422≈0.21\frac{5 - 4.58}{2} \approx \frac{0.42}{2} \approx 0.21.

More problems from Solve a quadratic equation using the quadratic formula

Question
The function h(t)=−16t2+144h(t) = -16t^{2} + 144 represents the height, h(t)h(t), in feet, of an object from the ground at tt seconds after it is dropped. A realistic domain (for time) for this function is:\newline(A)(A) −3≤t≤3-3 \leq t \leq 3\newline(B)(B) 0≤t≤30 \leq t \leq 3\newline(C)(C) 0≤h≤1440 \leq h \leq 144\newline(D)(D) all real numbers
Get tutor helpright-arrow

Posted 3 months ago

Question
Деление с остатком
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve the system of equations.\newliney=x2+40x−20y = x^2 + 40x - 20\newliney=40x−4y = 40x - 4\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve the system of equations.\newliney=−36x+26y = -36x + 26\newliney=x2−46x−13y = x^2 - 46x - 13\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve the system of equations.\newliney=32x2+32x−23y = 32x^2 + 32x - 23\newliney=32x+9y = 32x + 9\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve the system of equations.\newliney=x2+12x−41y = x^2 + 12x - 41\newliney=17x+9y = 17x + 9\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve the system of equations.\newliney=x2−43x−14y = x^2 - 43x - 14\newliney=−45x+34y = -45x + 34\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve the system of equations.\newliney=14x−26y = 14x - 26\newliney=2x2+14x−34y = 2x^2 + 14x - 34\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the discriminant.\newline3u2−8u+4=03u^2 - 8u + 4 = 0
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the discriminant.\newline7w2+5w+8=07w^2 + 5w + 8 = 0
Get tutor helpright-arrow

Posted 2 months ago

View all (21)