2x^2=19x-10

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Solution for 2x^2=19x-10 equation:


Simplifying
2x2 = 19x + -10

Reorder the terms:
2x2 = -10 + 19x

Solving
2x2 = -10 + 19x

Solving for variable 'x'.

Reorder the terms:
10 + -19x + 2x2 = -10 + 19x + 10 + -19x

Reorder the terms:
10 + -19x + 2x2 = -10 + 10 + 19x + -19x

Combine like terms: -10 + 10 = 0
10 + -19x + 2x2 = 0 + 19x + -19x
10 + -19x + 2x2 = 19x + -19x

Combine like terms: 19x + -19x = 0
10 + -19x + 2x2 = 0

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

Divide each side by '2'.
5 + -9.5x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -9.5x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -9.5x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -9.5x + x2 = 0 + -5
-9.5x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-9.5x + x2 = -5

The x term is -9.5x.  Take half its coefficient (-4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
-9.5x + 22.5625 + x2 = -5 + 22.5625

Reorder the terms:
22.5625 + -9.5x + x2 = -5 + 22.5625

Combine like terms: -5 + 22.5625 = 17.5625
22.5625 + -9.5x + x2 = 17.5625

Factor a perfect square on the left side:
(x + -4.75)(x + -4.75) = 17.5625

Calculate the square root of the right side: 4.190763654

Break this problem into two subproblems by setting 
(x + -4.75) equal to 4.190763654 and -4.190763654.

Subproblem 1

x + -4.75 = 4.190763654 Simplifying x + -4.75 = 4.190763654 Reorder the terms: -4.75 + x = 4.190763654 Solving -4.75 + x = 4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 4.190763654 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 4.190763654 + 4.75 x = 4.190763654 + 4.75 Combine like terms: 4.190763654 + 4.75 = 8.940763654 x = 8.940763654 Simplifying x = 8.940763654

Subproblem 2

x + -4.75 = -4.190763654 Simplifying x + -4.75 = -4.190763654 Reorder the terms: -4.75 + x = -4.190763654 Solving -4.75 + x = -4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -4.190763654 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -4.190763654 + 4.75 x = -4.190763654 + 4.75 Combine like terms: -4.190763654 + 4.75 = 0.559236346 x = 0.559236346 Simplifying x = 0.559236346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.940763654, 0.559236346}

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