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Quadratic equationsAlgebraHigh schoolabout 1:06

Solve x^2 + 14x + 45 = 0: animated lesson

A narrated, step-by-step quadratic equations video lesson with captions. Final answer: x = -9 or x = -5.

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 (0.4 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Solving an equation
    x2+14 x+45=0{ x}^{2}+14~ x+45 = 0
  2. 2. Steps, part 1
    1. x2+14 x+45=0{ x}^{2}+14~ x+45 = 0
      Start with the equation
    2. x2+14x+45=0x^{2} + 14x + 45 = 0
      Move every term to one side to get standard form
    3. Δ=b2−4ac=142−4⋅1⋅45=16\Delta = b^2 - 4ac = 14^2 - 4 \cdot 1 \cdot 45 = 16
      Compute the discriminant
    4. Δ > 0, so there are two distinct real roots
  3. 3. Steps, part 2
    1. x=−b±Δ2a=−14±162=−14±42x = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{-14 \pm \sqrt{16}}{2} = \frac{-14 \pm 4}{2}
      Apply the quadratic formula
    2. x1=−14−42=−9,x2=−14+42=−5x_1 = \frac{-14 - 4}{2} = -9,\quad x_2 = \frac{-14 + 4}{2} = -5
      Simplify each root
    3. x2+14x+45=(x+9)(x+5)x^2 + 14x + 45 = (x + 9)(x + 5)
      Factored form
  4. 4. On the graph
    -12-11-10-9-8-7-6-5-4-3-2x = -9x = -5
    Each solution is where the graph of left side minus right side crosses zero.
  5. 5. The answer
    x1=−9,x2=−5x_1 = -9,\quad x_2 = -5

    Δ = 16; x = -9 or x = -5

  6. 6. Check
    • x = -9: left side = 0, right side = 0 ✓
    • x = -5: left side = 0, right side = 0 ✓

Transcript

The problem. Here is the problem: x squared plus 14x plus 45 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 each root. Factored form.

On the graph. Now look at the graph of the left side minus the right side. It crosses zero exactly at the solutions we found.

The answer. So the answer is x equals negative 9 or x equals negative 5. The quadratic formula gives every solution of ax squared plus bx plus c equals 0.

Check. x equals negative 9: left side equals 0, right side equals 0, which checks out. x equals negative 5: 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.

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Solve x^2 + 14x + 45 = 0: Animated Step-by-Step Lesson