10x^2-3x-22=0

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Solution for 10x^2-3x-22=0 equation:


Simplifying
10x2 + -3x + -22 = 0

Reorder the terms:
-22 + -3x + 10x2 = 0

Solving
-22 + -3x + 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'.
-2.2 + -0.3x + x2 = 0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + -0.3x + 2.2 + x2 = 0 + 2.2

Reorder the terms:
-2.2 + 2.2 + -0.3x + x2 = 0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + -0.3x + x2 = 0 + 2.2
-0.3x + x2 = 0 + 2.2

Combine like terms: 0 + 2.2 = 2.2
-0.3x + x2 = 2.2

The x term is -0.3x.  Take half its coefficient (-0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
-0.3x + 0.0225 + x2 = 2.2 + 0.0225

Reorder the terms:
0.0225 + -0.3x + x2 = 2.2 + 0.0225

Combine like terms: 2.2 + 0.0225 = 2.2225
0.0225 + -0.3x + x2 = 2.2225

Factor a perfect square on the left side:
(x + -0.15)(x + -0.15) = 2.2225

Calculate the square root of the right side: 1.490805152

Break this problem into two subproblems by setting 
(x + -0.15) equal to 1.490805152 and -1.490805152.

Subproblem 1

x + -0.15 = 1.490805152 Simplifying x + -0.15 = 1.490805152 Reorder the terms: -0.15 + x = 1.490805152 Solving -0.15 + x = 1.490805152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 1.490805152 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 1.490805152 + 0.15 x = 1.490805152 + 0.15 Combine like terms: 1.490805152 + 0.15 = 1.640805152 x = 1.640805152 Simplifying x = 1.640805152

Subproblem 2

x + -0.15 = -1.490805152 Simplifying x + -0.15 = -1.490805152 Reorder the terms: -0.15 + x = -1.490805152 Solving -0.15 + x = -1.490805152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -1.490805152 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -1.490805152 + 0.15 x = -1.490805152 + 0.15 Combine like terms: -1.490805152 + 0.15 = -1.340805152 x = -1.340805152 Simplifying x = -1.340805152

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.640805152, -1.340805152}

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