Questions: Solve. 25 x^2-16=0 x=

Transcript text: Solve. \[ \begin{array}{l} 25 x^{2}-16=0 \\ x=\square \end{array} \]

Solution

Solution Steps

To solve the quadratic equation \(25x^2 - 16 = 0\), we can follow these steps:

Isolate the \(x^2\) term by adding 16 to both sides.
Divide both sides by 25 to solve for \(x^2\).
Take the square root of both sides to solve for \(x\).

Step 1: Isolate the \(x^2\) Term

Starting with the equation: \[ 25x^2 - 16 = 0 \] we add \(16\) to both sides: \[ 25x^2 = 16 \]

Step 2: Solve for \(x^2\)

Next, we divide both sides by \(25\): \[ x^2 = \frac{16}{25} \]

Step 3: Take the Square Root

Taking the square root of both sides gives us: \[ x = \pm \sqrt{\frac{16}{25}} = \pm \frac{4}{5} \] This results in two solutions: \[ x_1 = 0.8 \quad \text{and} \quad x_2 = -0.8 \]

Final Answer

The solutions to the equation are: \[ \boxed{x = 0.8} \quad \text{and} \quad \boxed{x = -0.8} \]

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