4x^2-27x+10=0

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Solution for 4x^2-27x+10=0 equation:


Simplifying
4x2 + -27x + 10 = 0

Reorder the terms:
10 + -27x + 4x2 = 0

Solving
10 + -27x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
2.5 + -6.75x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -6.75x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -6.75x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -6.75x + x2 = 0 + -2.5
-6.75x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-6.75x + x2 = -2.5

The x term is -6.75x.  Take half its coefficient (-3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
-6.75x + 11.390625 + x2 = -2.5 + 11.390625

Reorder the terms:
11.390625 + -6.75x + x2 = -2.5 + 11.390625

Combine like terms: -2.5 + 11.390625 = 8.890625
11.390625 + -6.75x + x2 = 8.890625

Factor a perfect square on the left side:
(x + -3.375)(x + -3.375) = 8.890625

Calculate the square root of the right side: 2.98171511

Break this problem into two subproblems by setting 
(x + -3.375) equal to 2.98171511 and -2.98171511.

Subproblem 1

x + -3.375 = 2.98171511 Simplifying x + -3.375 = 2.98171511 Reorder the terms: -3.375 + x = 2.98171511 Solving -3.375 + x = 2.98171511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = 2.98171511 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 2.98171511 + 3.375 x = 2.98171511 + 3.375 Combine like terms: 2.98171511 + 3.375 = 6.35671511 x = 6.35671511 Simplifying x = 6.35671511

Subproblem 2

x + -3.375 = -2.98171511 Simplifying x + -3.375 = -2.98171511 Reorder the terms: -3.375 + x = -2.98171511 Solving -3.375 + x = -2.98171511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = -2.98171511 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -2.98171511 + 3.375 x = -2.98171511 + 3.375 Combine like terms: -2.98171511 + 3.375 = 0.39328489 x = 0.39328489 Simplifying x = 0.39328489

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.35671511, 0.39328489}

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