Solve a problem

DecimalsArithmeticElementary schoolabout 1:05

Calculate x^2 = 0.04: animated lesson

A narrated, step-by-step decimals video lesson with captions. Final answer: x = -1/5 or x = 1/5.

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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 (0.4 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Solving an equation
${ x}^{2} = 0.04$
2. Steps, part 1
1. ${ x}^{2} = 0.04$
  Start with the equation
2. $x^{2} - \frac{1}{25} = 0$
  Move every term to one side to get standard form
3. $\Delta = b^2 - 4ac = 0^2 - 4 \cdot 1 \cdot (-\frac{1}{25}) = \frac{4}{25}$
  Compute the discriminant
4. $25x^2 - 1 = 0$
  Multiply the equation by 25 to clear fractions (same roots)
3. Steps, part 2
1. Δ > 0, so there are two distinct real roots
2. $x = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{0 \pm \sqrt{100}}{50} = \frac{0 \pm 10}{50}$
  Apply the quadratic formula
3. $x_1 = \frac{0 - 10}{50} = -\frac{1}{5},\quad x_2 = \frac{0 + 10}{50} = \frac{1}{5}$
  Simplify each root
4. $x^2 - \frac{1}{25} = \frac{1}{25}(5x + 1)(5x - 1)$
  Factored form
4. The answer
$x_1 = -\frac{1}{5},\quad x_2 = \frac{1}{5}$
Δ = 0.16; x = -1/5 or x = 1/5
5. Check
- x = -0.2: left side = 0.04, right side = 0.04 ✓
- x = 0.2: left side = 0.04, right side = 0.04 ✓

Transcript

The problem. Here is the problem: x squared equals 0.04. 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. Multiply the equation by 25 to clear fractions (same roots).

Steps, part 2. delta greater than 0, so there are two distinct real roots. Apply the quadratic formula. Simplify each root. Factored form.

The answer. So the answer is x equals negative 1 over 5 or x equals 1 over 5. The quadratic formula gives every solution of ax squared plus bx plus c equals 0.

Check. x equals negative 0.2: left side equals 0.04, right side equals 0.04, which checks out. x equals 0.2: left side equals 0.04, right side equals 0.04, which checks out.

About decimals

Add, subtract, multiply and divide decimal numbers, keeping track of the decimal point.

Calculate x^2 = 0.04: Decimals Step-by-Step Lesson