4x^2+5=10x

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Solution for 4x^2+5=10x equation:


Simplifying
4x2 + 5 = 10x

Reorder the terms:
5 + 4x2 = 10x

Solving
5 + 4x2 = 10x

Solving for variable 'x'.

Reorder the terms:
5 + -10x + 4x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
5 + -10x + 4x2 = 0

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

Divide each side by '4'.
1.25 + -2.5x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -2.5x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -2.5x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -2.5x + x2 = 0 + -1.25
-2.5x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-2.5x + x2 = -1.25

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = -1.25 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = -1.25 + 1.5625

Combine like terms: -1.25 + 1.5625 = 0.3125
1.5625 + -2.5x + x2 = 0.3125

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(x + -1.25) equal to 0.559016994 and -0.559016994.

Subproblem 1

x + -1.25 = 0.559016994 Simplifying x + -1.25 = 0.559016994 Reorder the terms: -1.25 + x = 0.559016994 Solving -1.25 + x = 0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 0.559016994 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 0.559016994 + 1.25 x = 0.559016994 + 1.25 Combine like terms: 0.559016994 + 1.25 = 1.809016994 x = 1.809016994 Simplifying x = 1.809016994

Subproblem 2

x + -1.25 = -0.559016994 Simplifying x + -1.25 = -0.559016994 Reorder the terms: -1.25 + x = -0.559016994 Solving -1.25 + x = -0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -0.559016994 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -0.559016994 + 1.25 x = -0.559016994 + 1.25 Combine like terms: -0.559016994 + 1.25 = 0.690983006 x = 0.690983006 Simplifying x = 0.690983006

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.809016994, 0.690983006}

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