x^2+1.5x=10

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Solution for x^2+1.5x=10 equation: 


Simplifying
x2 + 1.5x = 10

Reorder the terms:
1.5x + x2 = 10

Solving
1.5x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 1.5x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 1.5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 1.5x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 1.5x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 1.5x + x2 = 0 + 10
1.5x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
1.5x + x2 = 10

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 10 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 10 + 0.5625

Combine like terms: 10 + 0.5625 = 10.5625
0.5625 + 1.5x + x2 = 10.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 10.5625

Calculate the square root of the right side: 3.25

Break this problem into two subproblems by setting 
(x + 0.75) equal to 3.25 and -3.25.


Subproblem 1
x + 0.75 = 3.25

Simplifying
x + 0.75 = 3.25

Reorder the terms:
0.75 + x = 3.25

Solving
0.75 + x = 3.25

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 3.25 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 3.25 + -0.75
x = 3.25 + -0.75

Combine like terms: 3.25 + -0.75 = 2.5
x = 2.5

Simplifying
x = 2.5


Subproblem 2
x + 0.75 = -3.25

Simplifying
x + 0.75 = -3.25

Reorder the terms:
0.75 + x = -3.25

Solving
0.75 + x = -3.25

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -3.25 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -3.25 + -0.75
x = -3.25 + -0.75

Combine like terms: -3.25 + -0.75 = -4
x = -4

Simplifying
x = -4


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.5, -4}

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