-4t(5t-5)+8t=7t-4

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Solution for -4t(5t-5)+8t=7t-4 equation:


Simplifying
-4t(5t + -5) + 8t = 7t + -4

Reorder the terms:
-4t(-5 + 5t) + 8t = 7t + -4
(-5 * -4t + 5t * -4t) + 8t = 7t + -4
(20t + -20t2) + 8t = 7t + -4

Reorder the terms:
20t + 8t + -20t2 = 7t + -4

Combine like terms: 20t + 8t = 28t
28t + -20t2 = 7t + -4

Reorder the terms:
28t + -20t2 = -4 + 7t

Solving
28t + -20t2 = -4 + 7t

Solving for variable 't'.

Reorder the terms:
4 + 28t + -7t + -20t2 = -4 + 7t + 4 + -7t

Combine like terms: 28t + -7t = 21t
4 + 21t + -20t2 = -4 + 7t + 4 + -7t

Reorder the terms:
4 + 21t + -20t2 = -4 + 4 + 7t + -7t

Combine like terms: -4 + 4 = 0
4 + 21t + -20t2 = 0 + 7t + -7t
4 + 21t + -20t2 = 7t + -7t

Combine like terms: 7t + -7t = 0
4 + 21t + -20t2 = 0

Begin completing the square.  Divide all terms by
-20 the coefficient of the squared term: 

Divide each side by '-20'.
-0.2 + -1.05t + t2 = 0.0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -1.05t + 0.2 + t2 = 0.0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -1.05t + t2 = 0.0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -1.05t + t2 = 0.0 + 0.2
-1.05t + t2 = 0.0 + 0.2

Combine like terms: 0.0 + 0.2 = 0.2
-1.05t + t2 = 0.2

The t term is -1.05t.  Take half its coefficient (-0.525).
Square it (0.275625) and add it to both sides.

Add '0.275625' to each side of the equation.
-1.05t + 0.275625 + t2 = 0.2 + 0.275625

Reorder the terms:
0.275625 + -1.05t + t2 = 0.2 + 0.275625

Combine like terms: 0.2 + 0.275625 = 0.475625
0.275625 + -1.05t + t2 = 0.475625

Factor a perfect square on the left side:
(t + -0.525)(t + -0.525) = 0.475625

Calculate the square root of the right side: 0.689655711

Break this problem into two subproblems by setting 
(t + -0.525) equal to 0.689655711 and -0.689655711.

Subproblem 1

t + -0.525 = 0.689655711 Simplifying t + -0.525 = 0.689655711 Reorder the terms: -0.525 + t = 0.689655711 Solving -0.525 + t = 0.689655711 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.525' to each side of the equation. -0.525 + 0.525 + t = 0.689655711 + 0.525 Combine like terms: -0.525 + 0.525 = 0.000 0.000 + t = 0.689655711 + 0.525 t = 0.689655711 + 0.525 Combine like terms: 0.689655711 + 0.525 = 1.214655711 t = 1.214655711 Simplifying t = 1.214655711

Subproblem 2

t + -0.525 = -0.689655711 Simplifying t + -0.525 = -0.689655711 Reorder the terms: -0.525 + t = -0.689655711 Solving -0.525 + t = -0.689655711 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.525' to each side of the equation. -0.525 + 0.525 + t = -0.689655711 + 0.525 Combine like terms: -0.525 + 0.525 = 0.000 0.000 + t = -0.689655711 + 0.525 t = -0.689655711 + 0.525 Combine like terms: -0.689655711 + 0.525 = -0.164655711 t = -0.164655711 Simplifying t = -0.164655711

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.214655711, -0.164655711}

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