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Chapter 17: Chapter 17

Problem 471

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Solve for \(x^{2}: 4 x^{2}-7=0\)

Short Answer

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The short answer to solve for \(x^2\) in the equation \(4x^2 - 7 = 0\) is \(x^2 = \frac{7}{4}\).
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Isolate the \(x^2\) term on one side of the equation

In order to isolate the \(x^2\) term, we first need to move the constant value to the other side of the equation. We can do this by adding 7 to both sides of the equation: \[4x^2 - 7 + 7 = 0 + 7\] This simplifies to: \[4x^2 = 7\]

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

Now that we have isolated the \(x^2\) term, we can solve for its value by dividing both sides of the equation by 4: \[\frac{4x^2}{4} = \frac{7}{4}\] This simplifies to: \[x^2 = \frac{7}{4}\] So, the value of \(x^2\) is \(\frac{7}{4}\).

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