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EastWind [94]
2 years ago
14

Consider the equation: 12x=13-x^212x=13−x 2 12, x, equals, 13, minus, x, squared 1) Rewrite the equation by completing the squar

e. Your equation should look like (x+c)^2=d(x+c) 2 =dleft parenthesis, x, plus, c, right parenthesis, squared, equals, d or (x-c)^2=d(x−c) 2 =dleft parenthesis, x, minus, c, right parenthesis, squared, equals, d. 2) What are the solutions to the equation
Mathematics
1 answer:
Flauer [41]2 years ago
6 0

Answer:

(x + 6)^2 = 49

x = 1    or x = -13

Step-by-step explanation:

Given

12x = 13 - x^2

Using Completing the Square

12x = 13 - x^2 ---- Add x^2 to both sides

x^2 + 12x = 13 - x^2 + x^2

x^2 + 12x = 13

Divide the coefficient of x by 2; then add the square to both sides

x^2 + 12x + 6^2 = 13 + 6^2

x^2 + 12x + 36 = 13 + 36

x^2 + 12x + 36 = 49

Factorize

x^2 + 6x + 6x + 36 = 49

x(x + 6) + 6(x + 6) = 49

(x + 6)(x + 6) = 49

(x + 6)^2 = 49

Hence, the equation is (x + 6)^2 = 49

Solving further

Take square root of both sides

(x + 6) = \sqrt{49}

x + 6 = \±7

x  = \±7- 6

This implies that

x = 7 - 6     or x = -7 -6

x = 1    or x = -13

HEnce, the solutions are x = 1    or x = -13

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