(x-3)(x+3)=2x^2+3x+29

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Solution for (x-3)(x+3)=2x^2+3x+29 equation:


Simplifying
(x + -3)(x + 3) = 2x2 + 3x + 29

Reorder the terms:
(-3 + x)(x + 3) = 2x2 + 3x + 29

Reorder the terms:
(-3 + x)(3 + x) = 2x2 + 3x + 29

Multiply (-3 + x) * (3 + x)
(-3(3 + x) + x(3 + x)) = 2x2 + 3x + 29
((3 * -3 + x * -3) + x(3 + x)) = 2x2 + 3x + 29
((-9 + -3x) + x(3 + x)) = 2x2 + 3x + 29
(-9 + -3x + (3 * x + x * x)) = 2x2 + 3x + 29
(-9 + -3x + (3x + x2)) = 2x2 + 3x + 29

Combine like terms: -3x + 3x = 0
(-9 + 0 + x2) = 2x2 + 3x + 29
(-9 + x2) = 2x2 + 3x + 29

Reorder the terms:
-9 + x2 = 29 + 3x + 2x2

Solving
-9 + x2 = 29 + 3x + 2x2

Solving for variable 'x'.

Reorder the terms:
-9 + -29 + -3x + x2 + -2x2 = 29 + 3x + 2x2 + -29 + -3x + -2x2

Combine like terms: -9 + -29 = -38
-38 + -3x + x2 + -2x2 = 29 + 3x + 2x2 + -29 + -3x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-38 + -3x + -1x2 = 29 + 3x + 2x2 + -29 + -3x + -2x2

Reorder the terms:
-38 + -3x + -1x2 = 29 + -29 + 3x + -3x + 2x2 + -2x2

Combine like terms: 29 + -29 = 0
-38 + -3x + -1x2 = 0 + 3x + -3x + 2x2 + -2x2
-38 + -3x + -1x2 = 3x + -3x + 2x2 + -2x2

Combine like terms: 3x + -3x = 0
-38 + -3x + -1x2 = 0 + 2x2 + -2x2
-38 + -3x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-38 + -3x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(38 + 3x + x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(38 + 3x + x2)' equal to zero and attempt to solve: Simplifying 38 + 3x + x2 = 0 Solving 38 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-38' to each side of the equation. 38 + 3x + -38 + x2 = 0 + -38 Reorder the terms: 38 + -38 + 3x + x2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + 3x + x2 = 0 + -38 3x + x2 = 0 + -38 Combine like terms: 0 + -38 = -38 3x + x2 = -38 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 = -38 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -38 + 2.25 Combine like terms: -38 + 2.25 = -35.75 2.25 + 3x + x2 = -35.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -35.75 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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