4x^2=39x-10

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Solution for 4x^2=39x-10 equation:


Simplifying
4x2 = 39x + -10

Reorder the terms:
4x2 = -10 + 39x

Solving
4x2 = -10 + 39x

Solving for variable 'x'.

Reorder the terms:
10 + -39x + 4x2 = -10 + 39x + 10 + -39x

Reorder the terms:
10 + -39x + 4x2 = -10 + 10 + 39x + -39x

Combine like terms: -10 + 10 = 0
10 + -39x + 4x2 = 0 + 39x + -39x
10 + -39x + 4x2 = 39x + -39x

Combine like terms: 39x + -39x = 0
10 + -39x + 4x2 = 0

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

Divide each side by '4'.
2.5 + -9.75x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -9.75x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -9.75x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -9.75x + x2 = 0 + -2.5
-9.75x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-9.75x + x2 = -2.5

The x term is -9.75x.  Take half its coefficient (-4.875).
Square it (23.765625) and add it to both sides.

Add '23.765625' to each side of the equation.
-9.75x + 23.765625 + x2 = -2.5 + 23.765625

Reorder the terms:
23.765625 + -9.75x + x2 = -2.5 + 23.765625

Combine like terms: -2.5 + 23.765625 = 21.265625
23.765625 + -9.75x + x2 = 21.265625

Factor a perfect square on the left side:
(x + -4.875)(x + -4.875) = 21.265625

Calculate the square root of the right side: 4.611466686

Break this problem into two subproblems by setting 
(x + -4.875) equal to 4.611466686 and -4.611466686.

Subproblem 1

x + -4.875 = 4.611466686 Simplifying x + -4.875 = 4.611466686 Reorder the terms: -4.875 + x = 4.611466686 Solving -4.875 + x = 4.611466686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = 4.611466686 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = 4.611466686 + 4.875 x = 4.611466686 + 4.875 Combine like terms: 4.611466686 + 4.875 = 9.486466686 x = 9.486466686 Simplifying x = 9.486466686

Subproblem 2

x + -4.875 = -4.611466686 Simplifying x + -4.875 = -4.611466686 Reorder the terms: -4.875 + x = -4.611466686 Solving -4.875 + x = -4.611466686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = -4.611466686 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = -4.611466686 + 4.875 x = -4.611466686 + 4.875 Combine like terms: -4.611466686 + 4.875 = 0.263533314 x = 0.263533314 Simplifying x = 0.263533314

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.486466686, 0.263533314}

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