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Quadratic equationsAlgebraHigh schoolabout 1:17

Solve 11x^2 + 24x + 11 = 0: animated lesson

A narrated, step-by-step quadratic equations video lesson with captions. Final answer: x = (-12 - √23)/11 ≈ -1.5268938 or x = (-12 + √23)/11 ≈ -0.65492441.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.5 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Solving an equation
$11~{ x}^{2}+24~ x+11 = 0$
2. Steps, part 1
1. $11~{ x}^{2}+24~ x+11 = 0$
  Start with the equation
2. $11x^{2} + 24x + 11 = 0$
  Move every term to one side to get standard form
3. $\Delta = b^2 - 4ac = 24^2 - 4 \cdot 11 \cdot 11 = 92$
  Compute the discriminant
4. Δ > 0, so there are two distinct real roots
3. Steps, part 2
1. $x = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{-24 \pm \sqrt{92}}{22}$
  Apply the quadratic formula
2. $\sqrt{92} = 2\sqrt{23}$
  Simplify the square root
3. $x = \frac{-12 \pm \sqrt{23}}{11}$
  Reduce the fraction
4. The answer
$x_1 = \frac{-12 - \sqrt{23}}{11} \approx -1.5268938,\quad x_2 = \frac{-12 + \sqrt{23}}{11} \approx -0.65492441$
Δ = 92; x = (-12 - √23)/11 ≈ -1.5268938 or x = (-12 + √23)/11 ≈ -0.65492441
5. Check
- x = -1.5268938: left side = 0, right side = 0 ✓
- x = -0.65492441: left side = 0, right side = 0 ✓

Transcript

The problem. Here is the problem: 11x squared plus 24x plus 11 equals 0. A quadratic equation in x: solve with the quadratic formula.

Steps, part 1. Start with the equation. Move every term to one side to get standard form. Compute the discriminant. delta greater than 0, so there are two distinct real roots.

Steps, part 2. Apply the quadratic formula. Simplify the square root. Reduce the fraction.

The answer. So the answer is x equals (negative 12 minus the square root of 23 over 11 approximately negative 1.5268938 or x equals (negative 12 plus the square root of 23 over 11 approximately negative 0.65492441. The quadratic formula gives every solution of ax squared plus bx plus c equals 0.

Check. x equals negative 1.5268938: left side equals 0, right side equals 0, which checks out. x equals negative 0.65492441: left side equals 0, right side equals 0, which checks out.

About quadratic equations

Solve quadratics by factoring, completing the square or the quadratic formula, including complex roots.

Solve 11x^2 + 24x + 11 = 0: Animated Step-by-Step Lesson