Question

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1) (x+3)²+(2x-4)(2x+4)=5x²+2
2) (x+2)² - (x-3)²=20
3)5x²-10x=0
4) x²-11x+10=0​

Answer 1

1) (x+3)² + (2x-4)(2x+4) = 5x² + 2

Expanding the equation:

x² + 6x + 9 + (2x-4)(2x+4) = 5x² + 2

Simplifying the right side:

x² + 6x + 9 + 4x² - 16 = 5x² + 2

Combining like terms:

5x² + 6x - 7 = 5x² + 2

Subtracting 5x² from both sides:

6x - 7 = 2

Adding 7 to both sides:

6x = 9

Dividing both sides by 6:

x = 9/6

Simplifying:

x = 3/2

2) (x+2)² - (x-3)² = 20

Using the difference of squares:

[(x+2) + (x-3)][(x+2) - (x-3)] = 20

Simplifying:

[2x - 1][6] = 20

Dividing both sides by 6:

2x - 1 = 20/6

Simplifying:

2x - 1 = 10/3

Adding 1 to both sides:

2x = 10/3 + 1

Simplifying:

2x = 10/3 + 3/3

2x = 13/3

Dividing both sides by 2:

x = 13/6

3) 5x² - 10x = 0

Factoring out a common factor:

5x(x - 2) = 0

Setting each factor equal to 0:

5x = 0 or x - 2 = 0

Solving for x in each equation:

x = 0 or x = 2

4) x² - 11x + 10 = 0

This equation can be factored as:

(x - 10)(x - 1) = 0

Setting each factor equal to 0:

x - 10 = 0 or x - 1 = 0

Solving for x in each equation:

x = 10 or x = 1