Solve a problem

Quadratic equationsAlgebraHigh schoolabout 1:13

Solve 2x^2 + x - 5 = 0: animated lesson

A narrated, step-by-step quadratic equations video lesson with captions. Final answer: x = (-1 - √41)/4 ≈ -1.8507811 or x = (-1 + √41)/4 ≈ 1.3507811.

SpeedLanguage

Chapters

Transcript

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
$2~{ x}^{2}+ x-5 = 0$
2. Steps, part 1
1. $2~{ x}^{2}+ x-5 = 0$
  Start with the equation
2. $2x^{2} + x - 5 = 0$
  Move every term to one side to get standard form
3. $\Delta = b^2 - 4ac = 1^2 - 4 \cdot 2 \cdot (-5) = 41$
  Compute the discriminant
4. Δ > 0, so there are two distinct real roots
3. Steps, part 2
1. $x = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{-1 \pm \sqrt{41}}{4}$
  Apply the quadratic formula
2. $\sqrt{41} = \sqrt{41}$
  Simplify the square root
3. $x = \frac{-1 \pm \sqrt{41}}{4}$
  Reduce the fraction
4. The answer
$x_1 = \frac{-1 - \sqrt{41}}{4} \approx -1.8507811,\quad x_2 = \frac{-1 + \sqrt{41}}{4} \approx 1.3507811$
Δ = 41; x = (-1 - √41)/4 ≈ -1.8507811 or x = (-1 + √41)/4 ≈ 1.3507811
5. Check
- x = -1.8507811: left side = 0, right side = 0 ✓
- x = 1.3507811: left side = 0, right side = 0 ✓

Transcript

The problem. Here is the problem: 2x squared plus x minus 5 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 1 minus the square root of 41 over 4 approximately negative 1.8507811 or x equals (negative 1 plus the square root of 41 over 4 approximately 1.3507811. The quadratic formula gives every solution of ax squared plus bx plus c equals 0.

Check. x equals negative 1.8507811: left side equals 0, right side equals 0, which checks out. x equals 1.3507811: 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 2x^2 + x - 5 = 0: Animated Step-by-Step Lesson