Simplifying
x2 + x + -3.75 = 0
Reorder the terms:
-3.75 + x + x2 = 0
Solving
-3.75 + x + x2 = 0
Solving for variable 'x'.
Begin completing the square.
Move the constant term to the right:
Add '3.75' to each side of the equation.
-3.75 + x + 3.75 + x2 = 0 + 3.75
Reorder the terms:
-3.75 + 3.75 + x + x2 = 0 + 3.75
Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x + x2 = 0 + 3.75
x + x2 = 0 + 3.75
Combine like terms: 0 + 3.75 = 3.75
x + x2 = 3.75
The x term is x. Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.
Add '0.25' to each side of the equation.
x + 0.25 + x2 = 3.75 + 0.25
Reorder the terms:
0.25 + x + x2 = 3.75 + 0.25
Combine like terms: 3.75 + 0.25 = 4
0.25 + x + x2 = 4
Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 4
Calculate the square root of the right side: 2
Break this problem into two subproblems by setting
(x + 0.5) equal to 2 and -2.
Subproblem 1
x + 0.5 = 2
Simplifying
x + 0.5 = 2
Reorder the terms:
0.5 + x = 2
Solving
0.5 + x = 2
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 2 + -0.5
Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2 + -0.5
x = 2 + -0.5
Combine like terms: 2 + -0.5 = 1.5
x = 1.5
Simplifying
x = 1.5
Subproblem 2
x + 0.5 = -2
Simplifying
x + 0.5 = -2
Reorder the terms:
0.5 + x = -2
Solving
0.5 + x = -2
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -2 + -0.5
Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2 + -0.5
x = -2 + -0.5
Combine like terms: -2 + -0.5 = -2.5
x = -2.5
Simplifying
x = -2.5
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5, -2.5}
