15t-1.86t^2=25

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Solution for 15t-1.86t^2=25 equation:


Simplifying
15t + -1.86t2 = 25

Solving
15t + -1.86t2 = 25

Solving for variable 't'.

Reorder the terms:
-25 + 15t + -1.86t2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 15t + -1.86t2 = 0

Begin completing the square.  Divide all terms by
-1.86 the coefficient of the squared term: 

Divide each side by '-1.86'.
13.44086022 + -8.064516129t + t2 = 0

Move the constant term to the right:

Add '-13.44086022' to each side of the equation.
13.44086022 + -8.064516129t + -13.44086022 + t2 = 0 + -13.44086022

Reorder the terms:
13.44086022 + -13.44086022 + -8.064516129t + t2 = 0 + -13.44086022

Combine like terms: 13.44086022 + -13.44086022 = 0.00000000
0.00000000 + -8.064516129t + t2 = 0 + -13.44086022
-8.064516129t + t2 = 0 + -13.44086022

Combine like terms: 0 + -13.44086022 = -13.44086022
-8.064516129t + t2 = -13.44086022

The t term is -8.064516129t.  Take half its coefficient (-4.032258065).
Square it (16.25910510) and add it to both sides.

Add '16.25910510' to each side of the equation.
-8.064516129t + 16.25910510 + t2 = -13.44086022 + 16.25910510

Reorder the terms:
16.25910510 + -8.064516129t + t2 = -13.44086022 + 16.25910510

Combine like terms: -13.44086022 + 16.25910510 = 2.81824488
16.25910510 + -8.064516129t + t2 = 2.81824488

Factor a perfect square on the left side:
(t + -4.032258065)(t + -4.032258065) = 2.81824488

Calculate the square root of the right side: 1.678762902

Break this problem into two subproblems by setting 
(t + -4.032258065) equal to 1.678762902 and -1.678762902.

Subproblem 1

t + -4.032258065 = 1.678762902 Simplifying t + -4.032258065 = 1.678762902 Reorder the terms: -4.032258065 + t = 1.678762902 Solving -4.032258065 + t = 1.678762902 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.032258065' to each side of the equation. -4.032258065 + 4.032258065 + t = 1.678762902 + 4.032258065 Combine like terms: -4.032258065 + 4.032258065 = 0.000000000 0.000000000 + t = 1.678762902 + 4.032258065 t = 1.678762902 + 4.032258065 Combine like terms: 1.678762902 + 4.032258065 = 5.711020967 t = 5.711020967 Simplifying t = 5.711020967

Subproblem 2

t + -4.032258065 = -1.678762902 Simplifying t + -4.032258065 = -1.678762902 Reorder the terms: -4.032258065 + t = -1.678762902 Solving -4.032258065 + t = -1.678762902 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.032258065' to each side of the equation. -4.032258065 + 4.032258065 + t = -1.678762902 + 4.032258065 Combine like terms: -4.032258065 + 4.032258065 = 0.000000000 0.000000000 + t = -1.678762902 + 4.032258065 t = -1.678762902 + 4.032258065 Combine like terms: -1.678762902 + 4.032258065 = 2.353495163 t = 2.353495163 Simplifying t = 2.353495163

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.711020967, 2.353495163}

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