-2x^2-0.5x-3=4.2x-5

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Solution for -2x^2-0.5x-3=4.2x-5 equation:


Simplifying
-2x2 + -0.5x + -3 = 4.2x + -5

Reorder the terms:
-3 + -0.5x + -2x2 = 4.2x + -5

Reorder the terms:
-3 + -0.5x + -2x2 = -5 + 4.2x

Solving
-3 + -0.5x + -2x2 = -5 + 4.2x

Solving for variable 'x'.

Reorder the terms:
-3 + 5 + -0.5x + -4.2x + -2x2 = -5 + 4.2x + 5 + -4.2x

Combine like terms: -3 + 5 = 2
2 + -0.5x + -4.2x + -2x2 = -5 + 4.2x + 5 + -4.2x

Combine like terms: -0.5x + -4.2x = -4.7x
2 + -4.7x + -2x2 = -5 + 4.2x + 5 + -4.2x

Reorder the terms:
2 + -4.7x + -2x2 = -5 + 5 + 4.2x + -4.2x

Combine like terms: -5 + 5 = 0
2 + -4.7x + -2x2 = 0 + 4.2x + -4.2x
2 + -4.7x + -2x2 = 4.2x + -4.2x

Combine like terms: 4.2x + -4.2x = 0.0
2 + -4.7x + -2x2 = 0.0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-1 + 2.35x + x2 = 0.0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2.35x + 1 + x2 = 0.0 + 1

Reorder the terms:
-1 + 1 + 2.35x + x2 = 0.0 + 1

Combine like terms: -1 + 1 = 0
0 + 2.35x + x2 = 0.0 + 1
2.35x + x2 = 0.0 + 1

Combine like terms: 0.0 + 1 = 1
2.35x + x2 = 1

The x term is 2.35x.  Take half its coefficient (1.175).
Square it (1.380625) and add it to both sides.

Add '1.380625' to each side of the equation.
2.35x + 1.380625 + x2 = 1 + 1.380625

Reorder the terms:
1.380625 + 2.35x + x2 = 1 + 1.380625

Combine like terms: 1 + 1.380625 = 2.380625
1.380625 + 2.35x + x2 = 2.380625

Factor a perfect square on the left side:
(x + 1.175)(x + 1.175) = 2.380625

Calculate the square root of the right side: 1.542927412

Break this problem into two subproblems by setting 
(x + 1.175) equal to 1.542927412 and -1.542927412.

Subproblem 1

x + 1.175 = 1.542927412 Simplifying x + 1.175 = 1.542927412 Reorder the terms: 1.175 + x = 1.542927412 Solving 1.175 + x = 1.542927412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.175' to each side of the equation. 1.175 + -1.175 + x = 1.542927412 + -1.175 Combine like terms: 1.175 + -1.175 = 0.000 0.000 + x = 1.542927412 + -1.175 x = 1.542927412 + -1.175 Combine like terms: 1.542927412 + -1.175 = 0.367927412 x = 0.367927412 Simplifying x = 0.367927412

Subproblem 2

x + 1.175 = -1.542927412 Simplifying x + 1.175 = -1.542927412 Reorder the terms: 1.175 + x = -1.542927412 Solving 1.175 + x = -1.542927412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.175' to each side of the equation. 1.175 + -1.175 + x = -1.542927412 + -1.175 Combine like terms: 1.175 + -1.175 = 0.000 0.000 + x = -1.542927412 + -1.175 x = -1.542927412 + -1.175 Combine like terms: -1.542927412 + -1.175 = -2.717927412 x = -2.717927412 Simplifying x = -2.717927412

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.367927412, -2.717927412}

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