2x^2=10x+3

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Solution for 2x^2=10x+3 equation:


Simplifying
2x2 = 10x + 3

Reorder the terms:
2x2 = 3 + 10x

Solving
2x2 = 3 + 10x

Solving for variable 'x'.

Reorder the terms:
-3 + -10x + 2x2 = 3 + 10x + -3 + -10x

Reorder the terms:
-3 + -10x + 2x2 = 3 + -3 + 10x + -10x

Combine like terms: 3 + -3 = 0
-3 + -10x + 2x2 = 0 + 10x + -10x
-3 + -10x + 2x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-3 + -10x + 2x2 = 0

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

Divide each side by '2'.
-1.5 + -5x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -5x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -5x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -5x + x2 = 0 + 1.5
-5x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-5x + x2 = 1.5

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 1.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 1.5 + 6.25

Combine like terms: 1.5 + 6.25 = 7.75
6.25 + -5x + x2 = 7.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 7.75

Calculate the square root of the right side: 2.783882181

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.783882181 and -2.783882181.

Subproblem 1

x + -2.5 = 2.783882181 Simplifying x + -2.5 = 2.783882181 Reorder the terms: -2.5 + x = 2.783882181 Solving -2.5 + x = 2.783882181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.783882181 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.783882181 + 2.5 x = 2.783882181 + 2.5 Combine like terms: 2.783882181 + 2.5 = 5.283882181 x = 5.283882181 Simplifying x = 5.283882181

Subproblem 2

x + -2.5 = -2.783882181 Simplifying x + -2.5 = -2.783882181 Reorder the terms: -2.5 + x = -2.783882181 Solving -2.5 + x = -2.783882181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.783882181 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.783882181 + 2.5 x = -2.783882181 + 2.5 Combine like terms: -2.783882181 + 2.5 = -0.283882181 x = -0.283882181 Simplifying x = -0.283882181

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.283882181, -0.283882181}

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