0=8x^2+33x+189

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Solution for 0=8x^2+33x+189 equation:


Simplifying
0 = 8x2 + 33x + 189

Reorder the terms:
0 = 189 + 33x + 8x2

Solving
0 = 189 + 33x + 8x2

Solving for variable 'x'.

Combine like terms: 0 + -189 = -189
-189 + -33x + -8x2 = 189 + 33x + 8x2 + -189 + -33x + -8x2

Reorder the terms:
-189 + -33x + -8x2 = 189 + -189 + 33x + -33x + 8x2 + -8x2

Combine like terms: 189 + -189 = 0
-189 + -33x + -8x2 = 0 + 33x + -33x + 8x2 + -8x2
-189 + -33x + -8x2 = 33x + -33x + 8x2 + -8x2

Combine like terms: 33x + -33x = 0
-189 + -33x + -8x2 = 0 + 8x2 + -8x2
-189 + -33x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-189 + -33x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(189 + 33x + 8x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(189 + 33x + 8x2)' equal to zero and attempt to solve: Simplifying 189 + 33x + 8x2 = 0 Solving 189 + 33x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 23.625 + 4.125x + x2 = 0 Move the constant term to the right: Add '-23.625' to each side of the equation. 23.625 + 4.125x + -23.625 + x2 = 0 + -23.625 Reorder the terms: 23.625 + -23.625 + 4.125x + x2 = 0 + -23.625 Combine like terms: 23.625 + -23.625 = 0.000 0.000 + 4.125x + x2 = 0 + -23.625 4.125x + x2 = 0 + -23.625 Combine like terms: 0 + -23.625 = -23.625 4.125x + x2 = -23.625 The x term is 4.125x. Take half its coefficient (2.0625). Square it (4.25390625) and add it to both sides. Add '4.25390625' to each side of the equation. 4.125x + 4.25390625 + x2 = -23.625 + 4.25390625 Reorder the terms: 4.25390625 + 4.125x + x2 = -23.625 + 4.25390625 Combine like terms: -23.625 + 4.25390625 = -19.37109375 4.25390625 + 4.125x + x2 = -19.37109375 Factor a perfect square on the left side: (x + 2.0625)(x + 2.0625) = -19.37109375 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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