=10x^2+2x-1243

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Solution for =10x^2+2x-1243 equation:


Simplifying
0 = 10x2 + 2x + -1243

Reorder the terms:
0 = -1243 + 2x + 10x2

Solving
0 = -1243 + 2x + 10x2

Solving for variable 'x'.

Combine like terms: 0 + 1243 = 1243
1243 + -2x + -10x2 = -1243 + 2x + 10x2 + 1243 + -2x + -10x2

Reorder the terms:
1243 + -2x + -10x2 = -1243 + 1243 + 2x + -2x + 10x2 + -10x2

Combine like terms: -1243 + 1243 = 0
1243 + -2x + -10x2 = 0 + 2x + -2x + 10x2 + -10x2
1243 + -2x + -10x2 = 2x + -2x + 10x2 + -10x2

Combine like terms: 2x + -2x = 0
1243 + -2x + -10x2 = 0 + 10x2 + -10x2
1243 + -2x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
1243 + -2x + -10x2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-124.3 + 0.2x + x2 = 0

Move the constant term to the right:

Add '124.3' to each side of the equation.
-124.3 + 0.2x + 124.3 + x2 = 0 + 124.3

Reorder the terms:
-124.3 + 124.3 + 0.2x + x2 = 0 + 124.3

Combine like terms: -124.3 + 124.3 = 0.0
0.0 + 0.2x + x2 = 0 + 124.3
0.2x + x2 = 0 + 124.3

Combine like terms: 0 + 124.3 = 124.3
0.2x + x2 = 124.3

The x term is 0.2x.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2x + 0.01 + x2 = 124.3 + 0.01

Reorder the terms:
0.01 + 0.2x + x2 = 124.3 + 0.01

Combine like terms: 124.3 + 0.01 = 124.31
0.01 + 0.2x + x2 = 124.31

Factor a perfect square on the left side:
(x + 0.1)(x + 0.1) = 124.31

Calculate the square root of the right side: 11.149439448

Break this problem into two subproblems by setting 
(x + 0.1) equal to 11.149439448 and -11.149439448.

Subproblem 1

x + 0.1 = 11.149439448 Simplifying x + 0.1 = 11.149439448 Reorder the terms: 0.1 + x = 11.149439448 Solving 0.1 + x = 11.149439448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 11.149439448 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 11.149439448 + -0.1 x = 11.149439448 + -0.1 Combine like terms: 11.149439448 + -0.1 = 11.049439448 x = 11.049439448 Simplifying x = 11.049439448

Subproblem 2

x + 0.1 = -11.149439448 Simplifying x + 0.1 = -11.149439448 Reorder the terms: 0.1 + x = -11.149439448 Solving 0.1 + x = -11.149439448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -11.149439448 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -11.149439448 + -0.1 x = -11.149439448 + -0.1 Combine like terms: -11.149439448 + -0.1 = -11.249439448 x = -11.249439448 Simplifying x = -11.249439448

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.049439448, -11.249439448}

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