3x+4=x^2+24x+144

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Solution for 3x+4=x^2+24x+144 equation:


Simplifying
3x + 4 = x2 + 24x + 144

Reorder the terms:
4 + 3x = x2 + 24x + 144

Reorder the terms:
4 + 3x = 144 + 24x + x2

Solving
4 + 3x = 144 + 24x + x2

Solving for variable 'x'.

Reorder the terms:
4 + -144 + 3x + -24x + -1x2 = 144 + 24x + x2 + -144 + -24x + -1x2

Combine like terms: 4 + -144 = -140
-140 + 3x + -24x + -1x2 = 144 + 24x + x2 + -144 + -24x + -1x2

Combine like terms: 3x + -24x = -21x
-140 + -21x + -1x2 = 144 + 24x + x2 + -144 + -24x + -1x2

Reorder the terms:
-140 + -21x + -1x2 = 144 + -144 + 24x + -24x + x2 + -1x2

Combine like terms: 144 + -144 = 0
-140 + -21x + -1x2 = 0 + 24x + -24x + x2 + -1x2
-140 + -21x + -1x2 = 24x + -24x + x2 + -1x2

Combine like terms: 24x + -24x = 0
-140 + -21x + -1x2 = 0 + x2 + -1x2
-140 + -21x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-140 + -21x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(140 + 21x + x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(140 + 21x + x2)' equal to zero and attempt to solve: Simplifying 140 + 21x + x2 = 0 Solving 140 + 21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-140' to each side of the equation. 140 + 21x + -140 + x2 = 0 + -140 Reorder the terms: 140 + -140 + 21x + x2 = 0 + -140 Combine like terms: 140 + -140 = 0 0 + 21x + x2 = 0 + -140 21x + x2 = 0 + -140 Combine like terms: 0 + -140 = -140 21x + x2 = -140 The x term is 21x. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x + 110.25 + x2 = -140 + 110.25 Reorder the terms: 110.25 + 21x + x2 = -140 + 110.25 Combine like terms: -140 + 110.25 = -29.75 110.25 + 21x + x2 = -29.75 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = -29.75 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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