Math, asked by XxZEHRILIBANDIxX, 1 month ago

11) Solve : 6x² - 1+9x+1=0 by completing square method.

Answers

Answered by hayarunnisamuhammedp
1

Answer:

Simplifying

6x2 + 9x + 1 = 0

Reorder the terms:

1 + 9x + 6x2 = 0

Solving

1 + 9x + 6x2 = 0

Solving for variable 'x'.

Begin completing the square. Divide all terms by

6 the coefficient of the squared term:

Divide each side by '6'.

0.1666666667 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.

0.1666666667 + 1.5x + -0.1666666667 + x2 = 0 + -0.1666666667

Reorder the terms:

0.1666666667 + -0.1666666667 + 1.5x + x2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000

0.0000000000 + 1.5x + x2 = 0 + -0.1666666667

1.5x + x2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667

1.5x + x2 = -0.1666666667

The x term is 1.5x. Take half its coefficient (0.75).

Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.

1.5x + 0.5625 + x2 = -0.1666666667 + 0.5625

Reorder the terms:

0.5625 + 1.5x + x2 = -0.1666666667 + 0.5625

Combine like terms: -0.1666666667 + 0.5625 = 0.3958333333

0.5625 + 1.5x + x2 = 0.3958333333

Factor a perfect square on the left side:

(x + 0.75)(x + 0.75) = 0.3958333333

Calculate the square root of the right side: 0.62915287

Break this problem into two subproblems by setting

(x + 0.75) equal to 0.62915287 and -0.62915287

Step-by-step explanation:

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