0=4x^2-16x+22

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Solution for 0=4x^2-16x+22 equation:


Simplifying
0 = 4x2 + -16x + 22

Reorder the terms:
0 = 22 + -16x + 4x2

Solving
0 = 22 + -16x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -22 = -22
-22 + 16x + -4x2 = 22 + -16x + 4x2 + -22 + 16x + -4x2

Reorder the terms:
-22 + 16x + -4x2 = 22 + -22 + -16x + 16x + 4x2 + -4x2

Combine like terms: 22 + -22 = 0
-22 + 16x + -4x2 = 0 + -16x + 16x + 4x2 + -4x2
-22 + 16x + -4x2 = -16x + 16x + 4x2 + -4x2

Combine like terms: -16x + 16x = 0
-22 + 16x + -4x2 = 0 + 4x2 + -4x2
-22 + 16x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-22 + 16x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + 8x + -2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-11 + 8x + -2x2)' equal to zero and attempt to solve: Simplifying -11 + 8x + -2x2 = 0 Solving -11 + 8x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 5.5 + -4x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -4x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -4x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -4x + x2 = 0 + -5.5 -4x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -4x + x2 = -5.5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -5.5 + 4 Reorder the terms: 4 + -4x + x2 = -5.5 + 4 Combine like terms: -5.5 + 4 = -1.5 4 + -4x + x2 = -1.5 Factor a perfect square on the left side: (x + -2)(x + -2) = -1.5 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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