Simplifying
3x2 + 5x + -7x + 3 + -5x2 + 2 = 0
Reorder the terms:
3 + 2 + 5x + -7x + 3x2 + -5x2 = 0
Combine like terms: 3 + 2 = 5
5 + 5x + -7x + 3x2 + -5x2 = 0
Combine like terms: 5x + -7x = -2x
5 + -2x + 3x2 + -5x2 = 0
Combine like terms: 3x2 + -5x2 = -2x2
5 + -2x + -2x2 = 0
Solving
5 + -2x + -2x2 = 0
Solving for variable 'x'.
Begin completing the square. Divide all terms by
-2 the coefficient of the squared term:
Divide each side by '-2'.
-2.5 + x + x2 = 0
Move the constant term to the right:
Add '2.5' to each side of the equation.
-2.5 + x + 2.5 + x2 = 0 + 2.5
Reorder the terms:
-2.5 + 2.5 + x + x2 = 0 + 2.5
Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x + x2 = 0 + 2.5
x + x2 = 0 + 2.5
Combine like terms: 0 + 2.5 = 2.5
x + x2 = 2.5
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.
+ 0.25 + x2 = 2.5 + 0.25
Combine like terms: + 0.25 = 1.25
1.25 + x2 = 2.5 + 0.25
Combine like terms: 2.5 + 0.25 = 2.75
1.25 + x2 = 2.75
Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 2.75
Calculate the square root of the right side: 1.658312395
Break this problem into two subproblems by setting
(x + 0.5) equal to 1.658312395 and -1.658312395.
Subproblem 1
x + 0.5 = 1.658312395
Simplifying
x + 0.5 = 1.658312395
Reorder the terms:
0.5 + x = 1.658312395
Solving
0.5 + x = 1.658312395
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 = 1.658312395 + -0.5
Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.658312395 + -0.5
x = 1.658312395 + -0.5
Combine like terms: 1.658312395 + -0.5 = 1.158312395
x = 1.158312395
Simplifying
x = 1.158312395
Subproblem 2
x + 0.5 = -1.658312395
Simplifying
x + 0.5 = -1.658312395
Reorder the terms:
0.5 + x = -1.658312395
Solving
0.5 + x = -1.658312395
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 = -1.658312395 + -0.5
Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.658312395 + -0.5
x = -1.658312395 + -0.5
Combine like terms: -1.658312395 + -0.5 = -2.158312395
x = -2.158312395
Simplifying
x = -2.158312395
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.158312395, -2.158312395}