-1.6x^2+x+35=0

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Solution for -1.6x^2+x+35=0 equation:


Simplifying
-1.6x2 + x + 35 = 0

Reorder the terms:
35 + x + -1.6x2 = 0

Solving
35 + x + -1.6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1.6 the coefficient of the squared term: 

Divide each side by '-1.6'.
-21.875 + -0.625x + x2 = 0

Move the constant term to the right:

Add '21.875' to each side of the equation.
-21.875 + -0.625x + 21.875 + x2 = 0 + 21.875

Reorder the terms:
-21.875 + 21.875 + -0.625x + x2 = 0 + 21.875

Combine like terms: -21.875 + 21.875 = 0.000
0.000 + -0.625x + x2 = 0 + 21.875
-0.625x + x2 = 0 + 21.875

Combine like terms: 0 + 21.875 = 21.875
-0.625x + x2 = 21.875

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.
-0.625x + 0.25 + x2 = 21.875 + 0.25

Reorder the terms:
0.25 + -0.625x + x2 = 21.875 + 0.25

Combine like terms: 21.875 + 0.25 = 22.125
0.25 + -0.625x + x2 = 22.125

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 22.125

Calculate the square root of the right side: 4.703721931

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.703721931 and -4.703721931.

Subproblem 1

x + 0.5 = 4.703721931 Simplifying x + 0.5 = 4.703721931 Reorder the terms: 0.5 + x = 4.703721931 Solving 0.5 + x = 4.703721931 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 = 4.703721931 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.703721931 + -0.5 x = 4.703721931 + -0.5 Combine like terms: 4.703721931 + -0.5 = 4.203721931 x = 4.203721931 Simplifying x = 4.203721931

Subproblem 2

x + 0.5 = -4.703721931 Simplifying x + 0.5 = -4.703721931 Reorder the terms: 0.5 + x = -4.703721931 Solving 0.5 + x = -4.703721931 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 = -4.703721931 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.703721931 + -0.5 x = -4.703721931 + -0.5 Combine like terms: -4.703721931 + -0.5 = -5.203721931 x = -5.203721931 Simplifying x = -5.203721931

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.203721931, -5.203721931}

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