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To solve the equation 252x² - 1 = 52 + 1, follow these steps:
1. Add 1 to both sides of the equation to simplify it:
252x² - 1 + 1 = 52 + 1 + 1
252x² = 54
2. Divide both sides by 252 to isolate x²:
252x² / 252 = 54 / 252
x² = 54 / 252
3. Simplify the right side of the equation:
x² = 0.2143
4. To find the value of x, take the square root of both sides (remembering that there are two possible solutions - positive and negative square roots):
x = ±√0.2143
5. Calculate the square root of 0.2143 to find the approximate values of x:
x ≈ ±0.4635
Therefore, the solutions to the equation 252x² - 1 = 52 + 1 are x ≈ 0.4635 and x ≈ -0.4635.
