Question

solve by completing square.... 6x^2+3x+24=0
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Answer 1

Step-by-step explanation:

Simplifying

6x2 + -3x + -24 = 0

Reorder the terms:

-24 + -3x + 6x2 = 0

Solving

-24 + -3x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.

3(-8 + -1x + 2x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-8 + -1x + 2x2)' equal to zero and attempt to solve:

Simplifying

-8 + -1x + 2x2 = 0

Solving

-8 + -1x + 2x2 = 0

Begin completing the square. Divide all terms by

2 the coefficient of the squared term:

Divide each side by '2'.

-4 + -0.5x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.

-4 + -0.5x + 4 + x2 = 0 + 4

Reorder the terms:

-4 + 4 + -0.5x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0

0 + -0.5x + x2 = 0 + 4

-0.5x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4

-0.5x + x2 = 4

The x term is -0.5x. Take half its coefficient (-0.25).

Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.

-0.5x + 0.0625 + x2 = 4 + 0.0625

Reorder the terms:

0.0625 + -0.5x + x2 = 4 + 0.0625

Combine like terms: 4 + 0.0625 = 4.0625

0.0625 + -0.5x + x2 = 4.0625

Factor a perfect square on the left side:

(x + -0.25)(x + -0.25) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting

(x + -0.25) equal to 2.015564437 and -2.015564437.