.5x(3+x)=140

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Solution for .5x(3+x)=140 equation:


Simplifying
0.5x(3 + x) = 140
(3 * 0.5x + x * 0.5x) = 140
(1.5x + 0.5x2) = 140

Solving
1.5x + 0.5x2 = 140

Solving for variable 'x'.

Reorder the terms:
-140 + 1.5x + 0.5x2 = 140 + -140

Combine like terms: 140 + -140 = 0
-140 + 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'.
-280 + 3x + x2 = 0

Move the constant term to the right:

Add '280' to each side of the equation.
-280 + 3x + 280 + x2 = 0 + 280

Reorder the terms:
-280 + 280 + 3x + x2 = 0 + 280

Combine like terms: -280 + 280 = 0
0 + 3x + x2 = 0 + 280
3x + x2 = 0 + 280

Combine like terms: 0 + 280 = 280
3x + x2 = 280

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 = 280 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 280 + 2.25

Combine like terms: 280 + 2.25 = 282.25
2.25 + 3x + x2 = 282.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 282.25

Calculate the square root of the right side: 16.800297616

Break this problem into two subproblems by setting 
(x + 1.5) equal to 16.800297616 and -16.800297616.

Subproblem 1

x + 1.5 = 16.800297616 Simplifying x + 1.5 = 16.800297616 Reorder the terms: 1.5 + x = 16.800297616 Solving 1.5 + x = 16.800297616 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 = 16.800297616 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 16.800297616 + -1.5 x = 16.800297616 + -1.5 Combine like terms: 16.800297616 + -1.5 = 15.300297616 x = 15.300297616 Simplifying x = 15.300297616

Subproblem 2

x + 1.5 = -16.800297616 Simplifying x + 1.5 = -16.800297616 Reorder the terms: 1.5 + x = -16.800297616 Solving 1.5 + x = -16.800297616 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 = -16.800297616 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -16.800297616 + -1.5 x = -16.800297616 + -1.5 Combine like terms: -16.800297616 + -1.5 = -18.300297616 x = -18.300297616 Simplifying x = -18.300297616

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.300297616, -18.300297616}

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