-0.5x^2+1.5x+2=1.68

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Solution for -0.5x^2+1.5x+2=1.68 equation:


Simplifying
-0.5x2 + 1.5x + 2 = 1.68

Reorder the terms:
2 + 1.5x + -0.5x2 = 1.68

Solving
2 + 1.5x + -0.5x2 = 1.68

Solving for variable 'x'.

Reorder the terms:
2 + -1.68 + 1.5x + -0.5x2 = 1.68 + -1.68

Combine like terms: 2 + -1.68 = 0.32
0.32 + 1.5x + -0.5x2 = 1.68 + -1.68

Combine like terms: 1.68 + -1.68 = 0.00
0.32 + 1.5x + -0.5x2 = 0.00

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
-0.64 + -3x + x2 = 0.0

Move the constant term to the right:

Add '0.64' to each side of the equation.
-0.64 + -3x + 0.64 + x2 = 0.0 + 0.64

Reorder the terms:
-0.64 + 0.64 + -3x + x2 = 0.0 + 0.64

Combine like terms: -0.64 + 0.64 = 0.00
0.00 + -3x + x2 = 0.0 + 0.64
-3x + x2 = 0.0 + 0.64

Combine like terms: 0.0 + 0.64 = 0.64
-3x + x2 = 0.64

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 0.64 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 0.64 + 2.25

Combine like terms: 0.64 + 2.25 = 2.89
2.25 + -3x + x2 = 2.89

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 2.89

Calculate the square root of the right side: 1.7

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.7 and -1.7.

Subproblem 1

x + -1.5 = 1.7 Simplifying x + -1.5 = 1.7 Reorder the terms: -1.5 + x = 1.7 Solving -1.5 + x = 1.7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.7 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.7 + 1.5 x = 1.7 + 1.5 Combine like terms: 1.7 + 1.5 = 3.2 x = 3.2 Simplifying x = 3.2

Subproblem 2

x + -1.5 = -1.7 Simplifying x + -1.5 = -1.7 Reorder the terms: -1.5 + x = -1.7 Solving -1.5 + x = -1.7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.7 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.7 + 1.5 x = -1.7 + 1.5 Combine like terms: -1.7 + 1.5 = -0.2 x = -0.2 Simplifying x = -0.2

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.2, -0.2}

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