(22x+20)+(x+1)+2x(15x-16)=

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Solution for (22x+20)+(x+1)+2x(15x-16)= equation:


Simplifying
(22x + 20) + (x + 1) + 2x(15x + -16) = 0

Reorder the terms:
(20 + 22x) + (x + 1) + 2x(15x + -16) = 0

Remove parenthesis around (20 + 22x)
20 + 22x + (x + 1) + 2x(15x + -16) = 0

Reorder the terms:
20 + 22x + (1 + x) + 2x(15x + -16) = 0

Remove parenthesis around (1 + x)
20 + 22x + 1 + x + 2x(15x + -16) = 0

Reorder the terms:
20 + 22x + 1 + x + 2x(-16 + 15x) = 0
20 + 22x + 1 + x + (-16 * 2x + 15x * 2x) = 0
20 + 22x + 1 + x + (-32x + 30x2) = 0

Reorder the terms:
20 + 1 + 22x + x + -32x + 30x2 = 0

Combine like terms: 20 + 1 = 21
21 + 22x + x + -32x + 30x2 = 0

Combine like terms: 22x + x = 23x
21 + 23x + -32x + 30x2 = 0

Combine like terms: 23x + -32x = -9x
21 + -9x + 30x2 = 0

Solving
21 + -9x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + -3x + 10x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(7 + -3x + 10x2)' equal to zero and attempt to solve: Simplifying 7 + -3x + 10x2 = 0 Solving 7 + -3x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.7 + -0.3x + x2 = 0.0 Move the constant term to the right: Add '-0.7' to each side of the equation. 0.7 + -0.3x + -0.7 + x2 = 0.0 + -0.7 Reorder the terms: 0.7 + -0.7 + -0.3x + x2 = 0.0 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + -0.3x + x2 = 0.0 + -0.7 -0.3x + x2 = 0.0 + -0.7 Combine like terms: 0.0 + -0.7 = -0.7 -0.3x + x2 = -0.7 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = -0.7 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = -0.7 + 0.0225 Combine like terms: -0.7 + 0.0225 = -0.6775 0.0225 + -0.3x + x2 = -0.6775 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = -0.6775 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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