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Radical equationsAlgebraHigh schoolabout 1:14

Solve sqrt(x - 3) = x - 4: animated lesson

A narrated, step-by-step radical equations video lesson with captions. Final answer: x ≈ 5.618033989.

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
    x−3=x−4\sqrt{ x-3} = x-4
  2. 2. Step by step
    1. x−3=x−4\sqrt{ x-3} = x-4
      Start with the equation
    2. f(x)=x−3+4−x=0f(x) = \sqrt{ x-3}+4- x = 0
      Rewrite as f(x) = 0
    3. This equation is not polynomial, so solve it numerically
    4. x≈5.618033989x \approx 5.618033989
      Found 1 solution in [−10⁹, 10⁹]
  3. 3. The answer
    x ≈ 5.618033989\text{x ≈ 5.618033989}

    x ≈ 5.618033989

  4. 4. Check
    • x = 5.618034: left side = 1.618034, right side = 1.618034 ✓

Transcript

The problem. Here is the problem: sqrt(x minus 3) equals x minus 4. Solve for x numerically (the equation contains functions such as sin, log or roots).

Step by step. Start with the equation. Rewrite as f(x) equals 0. This equation is not polynomial, so solve it numerically. Scan x from negative 10 to the power 9 to 10 to the power 9 for sign changes of f and for points where the graph touches the axis, then narrow each one down. Every root is checked by substituting it back. Found 1 solution in [−10 to the power 9, 10 to the power 9].

The answer. So the answer is x approximately 5.618033989. Values marked approximately are numerical approximations accurate to about 10 significant digits. Every value was checked by substitution.

Check. x equals 5.618034: left side equals 1.618034, right side equals 1.618034, which checks out.

About radical equations

Solve equations with square roots by isolating and squaring, then checking for extraneous roots.

More lessons like this

Solve sqrt(x - 3) = x - 4: Animated Step-by-Step Lesson