Home Lessons Calculators Worksheets Resources Feedback Algebra Tutors

Calculator Output

Simplifying
10t2 = t + 2

Reorder the terms:
10t2 = 2 + t

Solving
10t2 = 2 + t

Solving for variable 't'.

Reorder the terms:
-2 + -1t + 10t2 = 2 + t + -2 + -1t

Reorder the terms:
-2 + -1t + 10t2 = 2 + -2 + t + -1t

Combine like terms: 2 + -2 = 0
-2 + -1t + 10t2 = 0 + t + -1t
-2 + -1t + 10t2 = t + -1t

Combine like terms: t + -1t = 0
-2 + -1t + 10t2 = 0

Begin completing the square.  Divide all terms by
10 the coefficient of the squared term: 

Divide each side by '10'.
-0.2 + -0.1t + t2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -0.1t + 0.2 + t2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -0.1t + t2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -0.1t + t2 = 0 + 0.2
-0.1t + t2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-0.1t + t2 = 0.2

The t term is -0.1t.  Take half its coefficient (-0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
-0.1t + 0.0025 + t2 = 0.2 + 0.0025

Reorder the terms:
0.0025 + -0.1t + t2 = 0.2 + 0.0025

Combine like terms: 0.2 + 0.0025 = 0.2025
0.0025 + -0.1t + t2 = 0.2025

Factor a perfect square on the left side:
(t + -0.05)(t + -0.05) = 0.2025

Calculate the square root of the right side: 0.45

Break this problem into two subproblems by setting 
(t + -0.05) equal to 0.45 and -0.45.

Subproblem 1

t + -0.05 = 0.45 Simplifying t + -0.05 = 0.45 Reorder the terms: -0.05 + t = 0.45 Solving -0.05 + t = 0.45 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + t = 0.45 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + t = 0.45 + 0.05 t = 0.45 + 0.05 Combine like terms: 0.45 + 0.05 = 0.5 t = 0.5 Simplifying t = 0.5

Subproblem 2

t + -0.05 = -0.45 Simplifying t + -0.05 = -0.45 Reorder the terms: -0.05 + t = -0.45 Solving -0.05 + t = -0.45 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + t = -0.45 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + t = -0.45 + 0.05 t = -0.45 + 0.05 Combine like terms: -0.45 + 0.05 = -0.4 t = -0.4 Simplifying t = -0.4

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.5, -0.4}
Processing time: 1 ms. 51435594 equations since February 08, 2004.   Disclaimer

Completing the Square Calculator

Equation: Variable:
       
Hint: Selecting "AUTO" in the variable box will make the calculator automatically solve for the first variable it sees.

Home Lessons Calculators Worksheets Resources Feedback Algebra Tutors