Explain how to solve 5x² - 3x = 25 by completing the square. What are the solutions?

Solution:

Given, the expression is 5x² - 3x = 25.

We know, (a² - b²) = (a + b)(a - b) --- (1)

5x² - 3x = 25 is rewritten as 5(x² - 3x/5) = 25

By completing the square, we create a perfect square trinomial on the LHS

Now, add the term 9/100 in LHS and 9/20 in RHS.

5(x² - 3x/5 + 9/100) = 25 + 9/20

5(x² - 3x/5 + 9/100) = (500 + 9)/20

5(x² - 3x/5 + 9/100) = 509/20

x² - 3x/5 + 9/100 = 509/100

Converting to standard form (1)

(x - 3/10)² = 509/100

Taking square root,

(x - 3/10) = √(509/100)

(x - 3/10) = ± (√509)/10

When (x - 3/10) = +√509/10

x = (3/10) + (√509/10)

x = (3 + √509)/10

x = (3 + 22.56)/10

x = 25.56/10

x = 2.556

When x = (3/10) - (√509/10)

x = (3 - √509)/10

x = (3 - 22.56)/10

x = -19.56/10

x = -1.956

Therefore, the solutions are -1.956 and 2.556

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Explain how to solve 5x² - 3x = 25 by completing the square. What are the solutions?

Summary:

By solving 5x² - 3x = 25 by completing the square, the solutions are x = -1.9567 and x = 2.556