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