2x(x+5)=4(x+1)

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Solution for 2x(x+5)=4(x+1) equation:


Simplifying
2x(x + 5) = 4(x + 1)

Reorder the terms:
2x(5 + x) = 4(x + 1)
(5 * 2x + x * 2x) = 4(x + 1)
(10x + 2x2) = 4(x + 1)

Reorder the terms:
10x + 2x2 = 4(1 + x)
10x + 2x2 = (1 * 4 + x * 4)
10x + 2x2 = (4 + 4x)

Solving
10x + 2x2 = 4 + 4x

Solving for variable 'x'.

Reorder the terms:
-4 + 10x + -4x + 2x2 = 4 + 4x + -4 + -4x

Combine like terms: 10x + -4x = 6x
-4 + 6x + 2x2 = 4 + 4x + -4 + -4x

Reorder the terms:
-4 + 6x + 2x2 = 4 + -4 + 4x + -4x

Combine like terms: 4 + -4 = 0
-4 + 6x + 2x2 = 0 + 4x + -4x
-4 + 6x + 2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-4 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 3x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-2 + 3x + x2)' equal to zero and attempt to solve: Simplifying -2 + 3x + x2 = 0 Solving -2 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 3x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 3x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3x + x2 = 0 + 2 3x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 3x + x2 = 2 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 2 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 2 + 2.25 Combine like terms: 2 + 2.25 = 4.25 2.25 + 3x + x2 = 4.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + 1.5) equal to 2.061552813 and -2.061552813.

Subproblem 1

x + 1.5 = 2.061552813 Simplifying x + 1.5 = 2.061552813 Reorder the terms: 1.5 + x = 2.061552813 Solving 1.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.061552813 + -1.5 x = 2.061552813 + -1.5 Combine like terms: 2.061552813 + -1.5 = 0.561552813 x = 0.561552813 Simplifying x = 0.561552813

Subproblem 2

x + 1.5 = -2.061552813 Simplifying x + 1.5 = -2.061552813 Reorder the terms: 1.5 + x = -2.061552813 Solving 1.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.061552813 + -1.5 x = -2.061552813 + -1.5 Combine like terms: -2.061552813 + -1.5 = -3.561552813 x = -3.561552813 Simplifying x = -3.561552813

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.561552813, -3.561552813}

Solution

x = {0.561552813, -3.561552813}

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