(2x+3)(2x+3)+49=0

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Solution for (2x+3)(2x+3)+49=0 equation:


Simplifying
(2x + 3)(2x + 3) + 49 = 0

Reorder the terms:
(3 + 2x)(2x + 3) + 49 = 0

Reorder the terms:
(3 + 2x)(3 + 2x) + 49 = 0

Multiply (3 + 2x) * (3 + 2x)
(3(3 + 2x) + 2x * (3 + 2x)) + 49 = 0
((3 * 3 + 2x * 3) + 2x * (3 + 2x)) + 49 = 0
((9 + 6x) + 2x * (3 + 2x)) + 49 = 0
(9 + 6x + (3 * 2x + 2x * 2x)) + 49 = 0
(9 + 6x + (6x + 4x2)) + 49 = 0

Combine like terms: 6x + 6x = 12x
(9 + 12x + 4x2) + 49 = 0

Reorder the terms:
9 + 49 + 12x + 4x2 = 0

Combine like terms: 9 + 49 = 58
58 + 12x + 4x2 = 0

Solving
58 + 12x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(29 + 6x + 2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(29 + 6x + 2x2)' equal to zero and attempt to solve: Simplifying 29 + 6x + 2x2 = 0 Solving 29 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 14.5 + 3x + x2 = 0 Move the constant term to the right: Add '-14.5' to each side of the equation. 14.5 + 3x + -14.5 + x2 = 0 + -14.5 Reorder the terms: 14.5 + -14.5 + 3x + x2 = 0 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + 3x + x2 = 0 + -14.5 3x + x2 = 0 + -14.5 Combine like terms: 0 + -14.5 = -14.5 3x + x2 = -14.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -14.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -14.5 + 2.25 Combine like terms: -14.5 + 2.25 = -12.25 2.25 + 3x + x2 = -12.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -12.25 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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