4x^2-68x+204=0

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Solution for 4x^2-68x+204=0 equation:


Simplifying
4x2 + -68x + 204 = 0

Reorder the terms:
204 + -68x + 4x2 = 0

Solving
204 + -68x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(51 + -17x + x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(51 + -17x + x2)' equal to zero and attempt to solve: Simplifying 51 + -17x + x2 = 0 Solving 51 + -17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-51' to each side of the equation. 51 + -17x + -51 + x2 = 0 + -51 Reorder the terms: 51 + -51 + -17x + x2 = 0 + -51 Combine like terms: 51 + -51 = 0 0 + -17x + x2 = 0 + -51 -17x + x2 = 0 + -51 Combine like terms: 0 + -51 = -51 -17x + x2 = -51 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -51 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -51 + 72.25 Combine like terms: -51 + 72.25 = 21.25 72.25 + -17x + x2 = 21.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x + -8.5) equal to 4.609772229 and -4.609772229.

Subproblem 1

x + -8.5 = 4.609772229 Simplifying x + -8.5 = 4.609772229 Reorder the terms: -8.5 + x = 4.609772229 Solving -8.5 + x = 4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 4.609772229 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 4.609772229 + 8.5 x = 4.609772229 + 8.5 Combine like terms: 4.609772229 + 8.5 = 13.109772229 x = 13.109772229 Simplifying x = 13.109772229

Subproblem 2

x + -8.5 = -4.609772229 Simplifying x + -8.5 = -4.609772229 Reorder the terms: -8.5 + x = -4.609772229 Solving -8.5 + x = -4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -4.609772229 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -4.609772229 + 8.5 x = -4.609772229 + 8.5 Combine like terms: -4.609772229 + 8.5 = 3.890227771 x = 3.890227771 Simplifying x = 3.890227771

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.109772229, 3.890227771}

Solution

x = {13.109772229, 3.890227771}

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