-5x^2+9x-2=0

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Solution for -5x^2+9x-2=0 equation:


Simplifying
-5x2 + 9x + -2 = 0

Reorder the terms:
-2 + 9x + -5x2 = 0

Solving
-2 + 9x + -5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
0.4 + -1.8x + x2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -1.8x + -0.4 + x2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -1.8x + x2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -1.8x + x2 = 0 + -0.4
-1.8x + x2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-1.8x + x2 = -0.4

The x term is -1.8x.  Take half its coefficient (-0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
-1.8x + 0.81 + x2 = -0.4 + 0.81

Reorder the terms:
0.81 + -1.8x + x2 = -0.4 + 0.81

Combine like terms: -0.4 + 0.81 = 0.41
0.81 + -1.8x + x2 = 0.41

Factor a perfect square on the left side:
(x + -0.9)(x + -0.9) = 0.41

Calculate the square root of the right side: 0.640312424

Break this problem into two subproblems by setting 
(x + -0.9) equal to 0.640312424 and -0.640312424.

Subproblem 1

x + -0.9 = 0.640312424 Simplifying x + -0.9 = 0.640312424 Reorder the terms: -0.9 + x = 0.640312424 Solving -0.9 + x = 0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 0.640312424 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 0.640312424 + 0.9 x = 0.640312424 + 0.9 Combine like terms: 0.640312424 + 0.9 = 1.540312424 x = 1.540312424 Simplifying x = 1.540312424

Subproblem 2

x + -0.9 = -0.640312424 Simplifying x + -0.9 = -0.640312424 Reorder the terms: -0.9 + x = -0.640312424 Solving -0.9 + x = -0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = -0.640312424 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -0.640312424 + 0.9 x = -0.640312424 + 0.9 Combine like terms: -0.640312424 + 0.9 = 0.259687576 x = 0.259687576 Simplifying x = 0.259687576

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.540312424, 0.259687576}

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