Solve 2x² + 3x - 7 = x² + 5x + 39 for x.

Solution:

Given, 2x² + 3x - 7 = x² + 5x + 39.

We have to solve for x.

By grouping of common terms,

2x² - x² + 3x - 5x - 7 - 39 = 0

(2 - 1)x² + (3 - 5)x - 46 = 0

x² - 2x - 46 = 0

Using quadratic formula,

x = -b ± √(b² - 4ac) / 2a

Here, a = 1, b = -2 and c = -46

x = -(-2) ± √((-2)² - 4(1)(-46)) / 2(1)

= 2 ± √ (4 + 4(46)) / 2

= 2 ± √4(1 + 46) / 2

= 2 ± 2√47 / 2

= 2(1 ± √47) / 2

= 1 ± √47

x = 1 + √47 and 1 - √47

Therefore, the value of x is 1 + √47, 1 - √47.

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Solve 2x² + 3x - 7 = x² + 5x + 39 for x.

Summary:

2x² + 3x - 7 = x² + 5x + 39 for x = 1 + √47, 1 - √47.