1-0.8451x-0.1373x^2=0

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Solution for 1-0.8451x-0.1373x^2=0 equation:


Simplifying
1 + -0.8451x + -0.1373x2 = 0

Solving
1 + -0.8451x + -0.1373x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.1373 the coefficient of the squared term: 

Divide each side by '-0.1373'.
-7.283321194 + 6.155134741x + x2 = 0

Move the constant term to the right:

Add '7.283321194' to each side of the equation.
-7.283321194 + 6.155134741x + 7.283321194 + x2 = 0 + 7.283321194

Reorder the terms:
-7.283321194 + 7.283321194 + 6.155134741x + x2 = 0 + 7.283321194

Combine like terms: -7.283321194 + 7.283321194 = 0.000000000
0.000000000 + 6.155134741x + x2 = 0 + 7.283321194
6.155134741x + x2 = 0 + 7.283321194

Combine like terms: 0 + 7.283321194 = 7.283321194
6.155134741x + x2 = 7.283321194

The x term is 6.155134741x.  Take half its coefficient (3.077567371).
Square it (9.471420923) and add it to both sides.

Add '9.471420923' to each side of the equation.
6.155134741x + 9.471420923 + x2 = 7.283321194 + 9.471420923

Reorder the terms:
9.471420923 + 6.155134741x + x2 = 7.283321194 + 9.471420923

Combine like terms: 7.283321194 + 9.471420923 = 16.754742117
9.471420923 + 6.155134741x + x2 = 16.754742117

Factor a perfect square on the left side:
(x + 3.077567371)(x + 3.077567371) = 16.754742117

Calculate the square root of the right side: 4.093255687

Break this problem into two subproblems by setting 
(x + 3.077567371) equal to 4.093255687 and -4.093255687.

Subproblem 1

x + 3.077567371 = 4.093255687 Simplifying x + 3.077567371 = 4.093255687 Reorder the terms: 3.077567371 + x = 4.093255687 Solving 3.077567371 + x = 4.093255687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.077567371' to each side of the equation. 3.077567371 + -3.077567371 + x = 4.093255687 + -3.077567371 Combine like terms: 3.077567371 + -3.077567371 = 0.000000000 0.000000000 + x = 4.093255687 + -3.077567371 x = 4.093255687 + -3.077567371 Combine like terms: 4.093255687 + -3.077567371 = 1.015688316 x = 1.015688316 Simplifying x = 1.015688316

Subproblem 2

x + 3.077567371 = -4.093255687 Simplifying x + 3.077567371 = -4.093255687 Reorder the terms: 3.077567371 + x = -4.093255687 Solving 3.077567371 + x = -4.093255687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.077567371' to each side of the equation. 3.077567371 + -3.077567371 + x = -4.093255687 + -3.077567371 Combine like terms: 3.077567371 + -3.077567371 = 0.000000000 0.000000000 + x = -4.093255687 + -3.077567371 x = -4.093255687 + -3.077567371 Combine like terms: -4.093255687 + -3.077567371 = -7.170823058 x = -7.170823058 Simplifying x = -7.170823058

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.015688316, -7.170823058}

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