-10x^2+x+12=0

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Solution for -10x^2+x+12=0 equation:


Simplifying
-10x2 + x + 12 = 0

Reorder the terms:
12 + x + -10x2 = 0

Solving
12 + x + -10x2 = 0

Solving for variable 'x'.

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

Divide each side by '-10'.
-1.2 + -0.1x + x2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -0.1x + 1.2 + x2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -0.1x + x2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -0.1x + x2 = 0 + 1.2
-0.1x + x2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-0.1x + x2 = 1.2

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.1x + 0.25 + x2 = 1.2 + 0.25

Reorder the terms:
0.25 + -0.1x + x2 = 1.2 + 0.25

Combine like terms: 1.2 + 0.25 = 1.45
0.25 + -0.1x + x2 = 1.45

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.45

Calculate the square root of the right side: 1.204159458

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.204159458 and -1.204159458.

Subproblem 1

x + 0.5 = 1.204159458 Simplifying x + 0.5 = 1.204159458 Reorder the terms: 0.5 + x = 1.204159458 Solving 0.5 + x = 1.204159458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.204159458 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.204159458 + -0.5 x = 1.204159458 + -0.5 Combine like terms: 1.204159458 + -0.5 = 0.704159458 x = 0.704159458 Simplifying x = 0.704159458

Subproblem 2

x + 0.5 = -1.204159458 Simplifying x + 0.5 = -1.204159458 Reorder the terms: 0.5 + x = -1.204159458 Solving 0.5 + x = -1.204159458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.204159458 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.204159458 + -0.5 x = -1.204159458 + -0.5 Combine like terms: -1.204159458 + -0.5 = -1.704159458 x = -1.704159458 Simplifying x = -1.704159458

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.704159458, -1.704159458}

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