Answer:
1. x² - 7x = -1
2. -3x + 2 = 4x²
3. 6 + 3x² = -3x
4. 2x² = 9
5. 9x² - 5x = 5
6. 2(3x + 5) = x²
6x + 30 = x²
-x² + 6x + 30 = 0
7. 3(x - 2)² = 6
3(x - 2)(x - 2) = 6
3(x² - 4x + 4) = 6
3x² - 12x + 12 = 6
3x² - 12x + 12 - 6 = 0
3x² - 12x + 6 = 0
8. 8x² + 3 = -4x
9. 2x - 3 = 2(x - 1)²
2x - 3 = 2(x - 1)(x - 1)
2x - 3 = 2(x² - 2x + 1)
2x - 3 = 2x² - 4 + 2
2x - 3 = 2x² - 2
-2x² + 2x - 3 + 2
-2x² + 2x - 1 = 0
10. 6 = (3x + 1)²
6 = (3x + 1)(3x + 1)
6 = 9x² + 3x + 3x + 1
6 = 9x² + 6x + 1
-9x² - 6x + 6 - 1 = 0
-9x² - 6x + 5 = 0
11. (x - 8)(x + 5) = 14
x² + 5x - 8x - 40 = 14
x² - 3x - 40 - 14 = 0
x² - 3x - 54 = 0
12. (x - 4)² + 8 = 0
(x - 4)(x - 4) + 8 = 0
x² - 4x - 4x + 16 + 8 = 0
x² - 8x + 24 = 0
13. (2x + 7)(x - 1) = 0
2x² - 2x + 7x - 7 = 0
2x² + 5x - 7 = 0
14. (x + 7)(x - 7) = -3x
x² - 7x + 7x - 49 = -3x
x² - 49 = -3x
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Answers & Comments
Answer:
1. x² - 7x = -1
Standard Form : x² - 7x + 1 = 0
a = 1 , b = 7 , c = 1
2. -3x + 2 = 4x²
Standard Form : -4x² + 3x + 2 = 0
a = -4 , b = 3 , c = 2
3. 6 + 3x² = -3x
Standard Form : 3x² + 3x + 6 = 0
a = 3 , b = 3 , c = 6
4. 2x² = 9
Standard Form : 2x² - 9 = 0
a = 2 , b = 0 , c = -9
5. 9x² - 5x = 5
Standard Form : 9x² - 5x - 5 = 0
a = 9 , b = -5 , c = -5
6. 2(3x + 5) = x²
6x + 30 = x²
-x² + 6x + 30 = 0
Standard Form : -x² + 6x + 30 = 0
a = -1 , b = 6 , c = 30
7. 3(x - 2)² = 6
3(x - 2)(x - 2) = 6
3(x² - 4x + 4) = 6
3x² - 12x + 12 = 6
3x² - 12x + 12 - 6 = 0
3x² - 12x + 6 = 0
Standard Form : 3x² - 12x + 6 = 0
a = 3 , b = -12 , c = 6
8. 8x² + 3 = -4x
Standard Form : 8x² + 4x + 3 = 0
a = 8 , b = 4 , c = 3
9. 2x - 3 = 2(x - 1)²
2x - 3 = 2(x - 1)(x - 1)
2x - 3 = 2(x² - 2x + 1)
2x - 3 = 2x² - 4 + 2
2x - 3 = 2x² - 2
-2x² + 2x - 3 + 2
-2x² + 2x - 1 = 0
Standard Form : -2x² + 2x - 1 = 0
a = -2 , b = 2 , c = -1
10. 6 = (3x + 1)²
6 = (3x + 1)(3x + 1)
6 = 9x² + 3x + 3x + 1
6 = 9x² + 6x + 1
-9x² - 6x + 6 - 1 = 0
-9x² - 6x + 5 = 0
Standard Form : -9x² - 6x + 5 = 0
a = -9 , b = -6 , c = 5
11. (x - 8)(x + 5) = 14
x² + 5x - 8x - 40 = 14
x² - 3x - 40 - 14 = 0
x² - 3x - 54 = 0
Standard Form : x² - 3x - 54 = 0
a = 1 , b = -3 , c = -54
12. (x - 4)² + 8 = 0
(x - 4)(x - 4) + 8 = 0
x² - 4x - 4x + 16 + 8 = 0
x² - 8x + 24 = 0
Standard Form : x² - 8x + 24 = 0
a = 1 , b = -8 , c = 24
13. (2x + 7)(x - 1) = 0
2x² - 2x + 7x - 7 = 0
2x² + 5x - 7 = 0
Standard Form : 2x² + 5x - 7 = 0
a = 2 , b = 5 , c = -7
14. (x + 7)(x - 7) = -3x
x² - 7x + 7x - 49 = -3x
x² - 49 = -3x
Standard Form : x² + 3x - 49 = 0
a = 1 , b = 3 , c = -49