z^2+ 0.5z+0.25 solve the equation
Answers
Answer:
Step-by-step explanation:
Simplifying
0 = x2 + -0.5x + 0.25
Reorder the terms:
0 = 0.25 + -0.5x + x2
Solving
0 = 0.25 + -0.5x + x2
Solving for variable 'x'.
Combine like terms: 0 + -0.25 = -0.25
-0.25 + 0.5x + -1x2 = 0.25 + -0.5x + x2 + -0.25 + 0.5x + -1x2
Reorder the terms:
-0.25 + 0.5x + -1x2 = 0.25 + -0.25 + -0.5x + 0.5x + x2 + -1x2
Combine like terms: 0.25 + -0.25 = 0.00
-0.25 + 0.5x + -1x2 = 0.00 + -0.5x + 0.5x + x2 + -1x2
-0.25 + 0.5x + -1x2 = -0.5x + 0.5x + x2 + -1x2
Combine like terms: -0.5x + 0.5x = 0.0
-0.25 + 0.5x + -1x2 = 0.0 + x2 + -1x2
-0.25 + 0.5x + -1x2 = x2 + -1x2
Combine like terms: x2 + -1x2 = 0
-0.25 + 0.5x + -1x2 = 0
Begin completing the square. Divide all terms by
-1 the coefficient of the squared term:
Divide each side by '-1'.
0.25 + -0.5x + x2 = 0
Move the constant term to the right:
Add '-0.25' to each side of the equation.
0.25 + -0.5x + -0.25 + x2 = 0 + -0.25
Reorder the terms:
0.25 + -0.25 + -0.5x + x2 = 0 + -0.25
Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -0.5x + x2 = 0 + -0.25
-0.5x + x2 = 0 + -0.25
Combine like terms: 0 + -0.25 = -0.25
-0.5x + x2 = -0.25
The x term is -0.5x. Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.
Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = -0.25 + 0.0625
Reorder the terms:
0.0625 + -0.5x + x2 = -0.25 + 0.0625
Combine like terms: -0.25 + 0.0625 = -0.1875
0.0625 + -0.5x + x2 = -0.1875
Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = -0.1875
Can't calculate square root of the right side.
The solution to this equation could not be determined.