Simplifying
x2 + 3x + -10 = 0
Reorder the terms:
-10 + 3x + x2 = 0
Solving
-10 + 3x + x2 = 0
Solving for variable 'x'.
Begin completing the square.
Move the constant term to the right:
Add '10' to each side of the equation.
-10 + 3x + 10 + x2 = 0 + 10
Reorder the terms:
-10 + 10 + 3x + x2 = 0 + 10
Combine like terms: -10 + 10 = 0
0 + 3x + x2 = 0 + 10
3x + x2 = 0 + 10
Combine like terms: 0 + 10 = 10
3x + x2 = 10
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 = 10 + 2.25
Reorder the terms:
2.25 + 3x + x2 = 10 + 2.25
Combine like terms: 10 + 2.25 = 12.25
2.25 + 3x + x2 = 12.25
Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 12.25
Calculate the square root of the right side: 3.5
Break this problem into two subproblems by setting
(x + 1.5) equal to 3.5 and -3.5.
Subproblem 1
x + 1.5 = 3.5
Simplifying
x + 1.5 = 3.5
Reorder the terms:
1.5 + x = 3.5
Solving
1.5 + x = 3.5
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 = 3.5 + -1.5
Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 3.5 + -1.5
x = 3.5 + -1.5
Combine like terms: 3.5 + -1.5 = 2
x = 2
Simplifying
x = 2
Subproblem 2
x + 1.5 = -3.5
Simplifying
x + 1.5 = -3.5
Reorder the terms:
1.5 + x = -3.5
Solving
1.5 + x = -3.5
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 = -3.5 + -1.5
Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -3.5 + -1.5
x = -3.5 + -1.5
Combine like terms: -3.5 + -1.5 = -5
x = -5
Simplifying
x = -5
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2, -5}
