2x+2=4x(x-5)

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Solution for 2x+2=4x(x-5) equation:


Simplifying
2x + 2 = 4x(x + -5)

Reorder the terms:
2 + 2x = 4x(x + -5)

Reorder the terms:
2 + 2x = 4x(-5 + x)
2 + 2x = (-5 * 4x + x * 4x)
2 + 2x = (-20x + 4x2)

Solving
2 + 2x = -20x + 4x2

Solving for variable 'x'.

Combine like terms: 2x + 20x = 22x
2 + 22x + -4x2 = -20x + 4x2 + 20x + -4x2

Reorder the terms:
2 + 22x + -4x2 = -20x + 20x + 4x2 + -4x2

Combine like terms: -20x + 20x = 0
2 + 22x + -4x2 = 0 + 4x2 + -4x2
2 + 22x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
2 + 22x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 11x + -2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(1 + 11x + -2x2)' equal to zero and attempt to solve: Simplifying 1 + 11x + -2x2 = 0 Solving 1 + 11x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + -5.5x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -5.5x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -5.5x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -5.5x + x2 = 0 + 0.5 -5.5x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -5.5x + x2 = 0.5 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = 0.5 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 0.5 + 7.5625 Combine like terms: 0.5 + 7.5625 = 8.0625 7.5625 + -5.5x + x2 = 8.0625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (x + -2.75) equal to 2.839454173 and -2.839454173.

Subproblem 1

x + -2.75 = 2.839454173 Simplifying x + -2.75 = 2.839454173 Reorder the terms: -2.75 + x = 2.839454173 Solving -2.75 + x = 2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 2.839454173 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 2.839454173 + 2.75 x = 2.839454173 + 2.75 Combine like terms: 2.839454173 + 2.75 = 5.589454173 x = 5.589454173 Simplifying x = 5.589454173

Subproblem 2

x + -2.75 = -2.839454173 Simplifying x + -2.75 = -2.839454173 Reorder the terms: -2.75 + x = -2.839454173 Solving -2.75 + x = -2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -2.839454173 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -2.839454173 + 2.75 x = -2.839454173 + 2.75 Combine like terms: -2.839454173 + 2.75 = -0.089454173 x = -0.089454173 Simplifying x = -0.089454173

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.589454173, -0.089454173}

Solution

x = {5.589454173, -0.089454173}

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