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.\newline2z2−7z+2=02z^2 - 7z + 2 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinez=z = _____ or z=z = _____

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.\newline2z2−7z+2=02z^2 - 7z + 2 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinez=z = _____ or z=z = _____
  1. Quadratic Formula: The quadratic formula is given by z=−b±b2−4ac2az = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients of the quadratic equation az2+bz+c=0az^2 + bz + c = 0. For the equation 2z2−7z+2=02z^2 - 7z + 2 = 0, we have a=2a = 2, b=−7b = -7, and c=2c = 2.
  2. Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. Here, it is (−7)2−4(2)(2)(-7)^2 - 4(2)(2).
  3. Discriminant Calculation: Perform the calculation: (−7)2−4(2)(2)=49−16=33(-7)^2 - 4(2)(2) = 49 - 16 = 33.
  4. Apply Quadratic Formula: Now, apply the quadratic formula with the calculated discriminant. The solutions for zz will be:\newlinez=−(−7)±332×2z = \frac{-(-7) \pm \sqrt{33}}{2 \times 2}\newlinez=7±334z = \frac{7 \pm \sqrt{33}}{4}
  5. First Solution: We have two solutions, corresponding to the '±\pm' in the formula. The first solution is when we use the '++' sign:\newlinez=7+334z = \frac{7 + \sqrt{33}}{4}
  6. Second Solution: The second solution is when we use the '-' sign: z=7−334z = \frac{7 - \sqrt{33}}{4}
  7. Decimal Approximations: These solutions cannot be simplified to integers or proper fractions. We can, however, express them as decimals rounded to the nearest hundredth. For the first solution:\newlinez≈(7+33)/4≈(7+5.74)/4≈12.74/4≈3.19z \approx (7 + \sqrt{33}) / 4 \approx (7 + 5.74) / 4 \approx 12.74 / 4 \approx 3.19
  8. Decimal Approximations: These solutions cannot be simplified to integers or proper fractions. We can, however, express them as decimals rounded to the nearest hundredth. For the first solution:\newlinez≈(7+33)/4≈(7+5.74)/4≈12.74/4≈3.19z \approx (7 + \sqrt{33}) / 4 \approx (7 + 5.74) / 4 \approx 12.74 / 4 \approx 3.19For the second solution:\newlinez≈(7−33)/4≈(7−5.74)/4≈1.26/4≈0.32z \approx (7 - \sqrt{33}) / 4 \approx (7 - 5.74) / 4 \approx 1.26 / 4 \approx 0.32

More problems from Solve a quadratic equation using the quadratic formula

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 (78)

Related topics

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