1(5)2(x-3)=4(x)1(x-5)

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Solution for 1(5)2(x-3)=4(x)1(x-5) equation:


Simplifying
1(5) * 2(x + -3) = 4(x) * 1(x + -5)

Reorder the terms:
1 * 5 * 2(-3 + x) = 4(x) * 1(x + -5)

Multiply 1 * 5
5 * 2(-3 + x) = 4(x) * 1(x + -5)

Multiply 5 * 2
10(-3 + x) = 4(x) * 1(x + -5)
(-3 * 10 + x * 10) = 4(x) * 1(x + -5)
(-30 + 10x) = 4(x) * 1(x + -5)

Reorder the terms:
-30 + 10x = 4x * 1(-5 + x)

Reorder the terms for easier multiplication:
-30 + 10x = 4 * 1x(-5 + x)

Multiply 4 * 1
-30 + 10x = 4x(-5 + x)
-30 + 10x = (-5 * 4x + x * 4x)
-30 + 10x = (-20x + 4x2)

Solving
-30 + 10x = -20x + 4x2

Solving for variable 'x'.

Combine like terms: 10x + 20x = 30x
-30 + 30x + -4x2 = -20x + 4x2 + 20x + -4x2

Reorder the terms:
-30 + 30x + -4x2 = -20x + 20x + 4x2 + -4x2

Combine like terms: -20x + 20x = 0
-30 + 30x + -4x2 = 0 + 4x2 + -4x2
-30 + 30x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-30 + 30x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 15x + -2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-15 + 15x + -2x2)' equal to zero and attempt to solve: Simplifying -15 + 15x + -2x2 = 0 Solving -15 + 15x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 7.5 + -7.5x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -7.5x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -7.5x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -7.5x + x2 = 0 + -7.5 -7.5x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -7.5x + x2 = -7.5 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = -7.5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = -7.5 + 14.0625 Combine like terms: -7.5 + 14.0625 = 6.5625 14.0625 + -7.5x + x2 = 6.5625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (x + -3.75) equal to 2.561737691 and -2.561737691.

Subproblem 1

x + -3.75 = 2.561737691 Simplifying x + -3.75 = 2.561737691 Reorder the terms: -3.75 + x = 2.561737691 Solving -3.75 + x = 2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 2.561737691 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 2.561737691 + 3.75 x = 2.561737691 + 3.75 Combine like terms: 2.561737691 + 3.75 = 6.311737691 x = 6.311737691 Simplifying x = 6.311737691

Subproblem 2

x + -3.75 = -2.561737691 Simplifying x + -3.75 = -2.561737691 Reorder the terms: -3.75 + x = -2.561737691 Solving -3.75 + x = -2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -2.561737691 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -2.561737691 + 3.75 x = -2.561737691 + 3.75 Combine like terms: -2.561737691 + 3.75 = 1.188262309 x = 1.188262309 Simplifying x = 1.188262309

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.311737691, 1.188262309}

Solution

x = {6.311737691, 1.188262309}

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