10x^2-9x-4=0

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Solution for 10x^2-9x-4=0 equation:


Simplifying
10x2 + -9x + -4 = 0

Reorder the terms:
-4 + -9x + 10x2 = 0

Solving
-4 + -9x + 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'.
-0.4 + -0.9x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -0.9x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -0.9x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -0.9x + x2 = 0 + 0.4
-0.9x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-0.9x + x2 = 0.4

The x term is -0.9x.  Take half its coefficient (-0.45).
Square it (0.2025) and add it to both sides.

Add '0.2025' to each side of the equation.
-0.9x + 0.2025 + x2 = 0.4 + 0.2025

Reorder the terms:
0.2025 + -0.9x + x2 = 0.4 + 0.2025

Combine like terms: 0.4 + 0.2025 = 0.6025
0.2025 + -0.9x + x2 = 0.6025

Factor a perfect square on the left side:
(x + -0.45)(x + -0.45) = 0.6025

Calculate the square root of the right side: 0.776208735

Break this problem into two subproblems by setting 
(x + -0.45) equal to 0.776208735 and -0.776208735.

Subproblem 1

x + -0.45 = 0.776208735 Simplifying x + -0.45 = 0.776208735 Reorder the terms: -0.45 + x = 0.776208735 Solving -0.45 + x = 0.776208735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = 0.776208735 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = 0.776208735 + 0.45 x = 0.776208735 + 0.45 Combine like terms: 0.776208735 + 0.45 = 1.226208735 x = 1.226208735 Simplifying x = 1.226208735

Subproblem 2

x + -0.45 = -0.776208735 Simplifying x + -0.45 = -0.776208735 Reorder the terms: -0.45 + x = -0.776208735 Solving -0.45 + x = -0.776208735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = -0.776208735 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = -0.776208735 + 0.45 x = -0.776208735 + 0.45 Combine like terms: -0.776208735 + 0.45 = -0.326208735 x = -0.326208735 Simplifying x = -0.326208735

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.226208735, -0.326208735}

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