.5x^2+1.5x=4

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Solution for .5x^2+1.5x=4 equation:


Simplifying
0.5x2 + 1.5x = 4

Reorder the terms:
1.5x + 0.5x2 = 4

Solving
1.5x + 0.5x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 1.5x + 0.5x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 1.5x + 0.5x2 = 0

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

Divide each side by '0.5'.
-8 + 3x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 3x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 3x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3x + x2 = 0 + 8
3x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
3x + x2 = 8

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 = 8 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 8 + 2.25

Combine like terms: 8 + 2.25 = 10.25
2.25 + 3x + x2 = 10.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.201562119 and -3.201562119.

Subproblem 1

x + 1.5 = 3.201562119 Simplifying x + 1.5 = 3.201562119 Reorder the terms: 1.5 + x = 3.201562119 Solving 1.5 + x = 3.201562119 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 = 3.201562119 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.201562119 + -1.5 x = 3.201562119 + -1.5 Combine like terms: 3.201562119 + -1.5 = 1.701562119 x = 1.701562119 Simplifying x = 1.701562119

Subproblem 2

x + 1.5 = -3.201562119 Simplifying x + 1.5 = -3.201562119 Reorder the terms: 1.5 + x = -3.201562119 Solving 1.5 + x = -3.201562119 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 = -3.201562119 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.201562119 + -1.5 x = -3.201562119 + -1.5 Combine like terms: -3.201562119 + -1.5 = -4.701562119 x = -4.701562119 Simplifying x = -4.701562119

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.701562119, -4.701562119}

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