15x-10=5x(x-2)

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Solution for 15x-10=5x(x-2) equation:


Simplifying
15x + -10 = 5x(x + -2)

Reorder the terms:
-10 + 15x = 5x(x + -2)

Reorder the terms:
-10 + 15x = 5x(-2 + x)
-10 + 15x = (-2 * 5x + x * 5x)
-10 + 15x = (-10x + 5x2)

Solving
-10 + 15x = -10x + 5x2

Solving for variable 'x'.

Combine like terms: 15x + 10x = 25x
-10 + 25x + -5x2 = -10x + 5x2 + 10x + -5x2

Reorder the terms:
-10 + 25x + -5x2 = -10x + 10x + 5x2 + -5x2

Combine like terms: -10x + 10x = 0
-10 + 25x + -5x2 = 0 + 5x2 + -5x2
-10 + 25x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-10 + 25x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + 5x + -1x2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-2 + 5x + -1x2)' equal to zero and attempt to solve: Simplifying -2 + 5x + -1x2 = 0 Solving -2 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -5x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5x + x2 = 0 + -2 -5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -5x + x2 = -2 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -2 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -2 + 6.25 Combine like terms: -2 + 6.25 = 4.25 6.25 + -5x + x2 = 4.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + -2.5) equal to 2.061552813 and -2.061552813.

Subproblem 1

x + -2.5 = 2.061552813 Simplifying x + -2.5 = 2.061552813 Reorder the terms: -2.5 + x = 2.061552813 Solving -2.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.061552813 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.061552813 + 2.5 x = 2.061552813 + 2.5 Combine like terms: 2.061552813 + 2.5 = 4.561552813 x = 4.561552813 Simplifying x = 4.561552813

Subproblem 2

x + -2.5 = -2.061552813 Simplifying x + -2.5 = -2.061552813 Reorder the terms: -2.5 + x = -2.061552813 Solving -2.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.061552813 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.061552813 + 2.5 x = -2.061552813 + 2.5 Combine like terms: -2.061552813 + 2.5 = 0.438447187 x = 0.438447187 Simplifying x = 0.438447187

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.561552813, 0.438447187}

Solution

x = {4.561552813, 0.438447187}

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