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Illusion [34]
3 years ago
12

Solve the quadratic equation by completing the square.

Mathematics
1 answer:
ivolga24 [154]3 years ago
6 0
X^2 - 10x + 15 = 0
x^2 - 10x = -15
x^2 - 10x + 25 = -15 + 25
(x - 5)^2 = 10 <====
x - 5 = (+-)sqrt 10
x = 5 (+-) sqrt 10

solutions are :
x = 5 + sqrt 10 and x = 5 - sqrt 10


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(2x-3y)(2x-3y)(2x-3y)(2x-3y)(2x-3y)

1st and 2nd power :
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= 4x² - 12xy + 9y²

3rd power:
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8x³ - 24x²y + 18xy² - 12x²y +36xy² - 27y³
8x³ - 24x²y - 12x²y + 18xy² + 36xy² - 27y³
8x³ - 36x²y + 54xy² - 27y³

4th power
(2x-3y)(8x³ - 36x²y + 54xy² - 27y³) = 2x(8x³ - 36x²y + 54xy² - 27y³) -3y(8x³ - 36x²y + 54xy² - 27y³) = 16x^4 - 72x³y + 108x²y² - 54xy³ - 24x³y + 108x²y² - 162xy³ + 81y^4
16x^4 - 72x³y - 24x³y + 108x²y² + 108x²y² - 54xy³ - 162xy³ + 81y^4
16x^4 - 96x³y + 216x²y² - 216xy³ + 81y^4

5th power
(2x-3y)(<span>16x^4 - 96x³y + 216x²y² - 216xy³ + 81y^4)
2x(</span>16x^4 - 96x³y + 216x²y² - 216xy³ + 81y^4) - 3y(<span>16x^4 - 96x³y + 216x²y² - 216xy³ + 81y^4)
= 32x^5 - 192x^4y + 432x</span>³y² - 432x²y³ + 162xy^4 - 48x^4y + 288x³y² - 648x²y³ + 648xy^4 - 243y^5

32x^5 - 192x^4y -48x^4y + 432x³y² + 288x³y² - 432x²y³ - 648x²y³ + 162xy^4 + 648xy^4 - 243y^5

32x^5 - 240x^4y + 720x³y² - 1,080x²y³ + 810xy^4 - 243y^5
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4 years ago
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