86400=(60x)*(x-7)

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Solution for 86400=(60x)*(x-7) equation:


Simplifying
86400 = (60x)(x + -7)

Remove parenthesis around (60x)
86400 = 60x(x + -7)

Reorder the terms:
86400 = 60x(-7 + x)
86400 = (-7 * 60x + x * 60x)
86400 = (-420x + 60x2)

Solving
86400 = -420x + 60x2

Solving for variable 'x'.

Reorder the terms:
86400 + 420x + -60x2 = -420x + 420x + 60x2 + -60x2

Combine like terms: -420x + 420x = 0
86400 + 420x + -60x2 = 0 + 60x2 + -60x2
86400 + 420x + -60x2 = 60x2 + -60x2

Combine like terms: 60x2 + -60x2 = 0
86400 + 420x + -60x2 = 0

Factor out the Greatest Common Factor (GCF), '60'.
60(1440 + 7x + -1x2) = 0

Ignore the factor 60.

Subproblem 1

Set the factor '(1440 + 7x + -1x2)' equal to zero and attempt to solve: Simplifying 1440 + 7x + -1x2 = 0 Solving 1440 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1440 + -7x + x2 = 0 Move the constant term to the right: Add '1440' to each side of the equation. -1440 + -7x + 1440 + x2 = 0 + 1440 Reorder the terms: -1440 + 1440 + -7x + x2 = 0 + 1440 Combine like terms: -1440 + 1440 = 0 0 + -7x + x2 = 0 + 1440 -7x + x2 = 0 + 1440 Combine like terms: 0 + 1440 = 1440 -7x + x2 = 1440 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 1440 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 1440 + 12.25 Combine like terms: 1440 + 12.25 = 1452.25 12.25 + -7x + x2 = 1452.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 1452.25 Calculate the square root of the right side: 38.108398025 Break this problem into two subproblems by setting (x + -3.5) equal to 38.108398025 and -38.108398025.

Subproblem 1

x + -3.5 = 38.108398025 Simplifying x + -3.5 = 38.108398025 Reorder the terms: -3.5 + x = 38.108398025 Solving -3.5 + x = 38.108398025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 38.108398025 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 38.108398025 + 3.5 x = 38.108398025 + 3.5 Combine like terms: 38.108398025 + 3.5 = 41.608398025 x = 41.608398025 Simplifying x = 41.608398025

Subproblem 2

x + -3.5 = -38.108398025 Simplifying x + -3.5 = -38.108398025 Reorder the terms: -3.5 + x = -38.108398025 Solving -3.5 + x = -38.108398025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -38.108398025 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -38.108398025 + 3.5 x = -38.108398025 + 3.5 Combine like terms: -38.108398025 + 3.5 = -34.608398025 x = -34.608398025 Simplifying x = -34.608398025

Solution

The solution to the problem is based on the solutions from the subproblems. x = {41.608398025, -34.608398025}

Solution

x = {41.608398025, -34.608398025}

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