Find value of t in 10t^2+10t-0.25?
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Step-by-step explanation:
10t^2+10t-0.25
Simplifying
10t2 + -10t + 2.5 = 0
Reorder the terms:
2.5 + -10t + 10t2 = 0
Solving
2.5 + -10t + 10t2 = 0
Solving for variable 't'.
Begin completing the square. Divide all terms by
10 the coefficient of the squared term:
Divide each side by '10'.
0.25 + -1t + t2 = 0
Move the constant term to the right:
Add '-0.25' to each side of the equation.
0.25 + -1t + -0.25 + t2 = 0 + -0.25
Reorder the terms:
0.25 + -0.25 + -1t + t2 = 0 + -0.25
Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1t + t2 = 0 + -0.25
-1t + t2 = 0 + -0.25
Combine like terms: 0 + -0.25 = -0.25
-1t + t2 = -0.25
The t term is -1t. 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.
-1t + 0.25 + t2 = -0.25 + 0.25
Reorder the terms:
0.25 + -1t + t2 = -0.25 + 0.25
Combine like terms: -0.25 + 0.25 = 0.00
0.25 + -1t + t2 = 0.00
Factor a perfect square on the left side:
(t + -0.5)(t + -0.5) = 0.00
Calculate the square root of the right side: 0.00
Break this problem into two subproblems by setting
(t + -0.5) equal to 0.00 and 0.00.
Subproblem 1
t + -0.5 = 0.00
Simplifying
t + -0.5 = 0.00
Reorder the terms:
-0.5 + t = 0.00
Solving
-0.5 + t = 0.00
Solving for variable 't'.
Move all terms containing t to the left, all other terms to the right.
Add '0.5' to each side of the equation.
-0.5 + 0.5 + t = 0.00 + 0.5
Combine like terms: -0.5 + 0.5 = 0.0
0.0 + t = 0.00 + 0.5
t = 0.00 + 0.5
Combine like terms: 0.00 + 0.5 = 0.5
t = 0.5
Simplifying
t = 0.5
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