5(x-3)-4(x+8)2x=

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Solution for 5(x-3)-4(x+8)2x= equation:


Simplifying
5(x + -3) + -4(x + 8) * 2x = 0

Reorder the terms:
5(-3 + x) + -4(x + 8) * 2x = 0
(-3 * 5 + x * 5) + -4(x + 8) * 2x = 0
(-15 + 5x) + -4(x + 8) * 2x = 0

Reorder the terms:
-15 + 5x + -4(8 + x) * 2x = 0

Reorder the terms for easier multiplication:
-15 + 5x + -4 * 2x(8 + x) = 0

Multiply -4 * 2
-15 + 5x + -8x(8 + x) = 0
-15 + 5x + (8 * -8x + x * -8x) = 0
-15 + 5x + (-64x + -8x2) = 0

Combine like terms: 5x + -64x = -59x
-15 + -59x + -8x2 = 0

Solving
-15 + -59x + -8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + 59x + 8x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(15 + 59x + 8x2)' equal to zero and attempt to solve: Simplifying 15 + 59x + 8x2 = 0 Solving 15 + 59x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.875 + 7.375x + x2 = 0 Move the constant term to the right: Add '-1.875' to each side of the equation. 1.875 + 7.375x + -1.875 + x2 = 0 + -1.875 Reorder the terms: 1.875 + -1.875 + 7.375x + x2 = 0 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + 7.375x + x2 = 0 + -1.875 7.375x + x2 = 0 + -1.875 Combine like terms: 0 + -1.875 = -1.875 7.375x + x2 = -1.875 The x term is 7.375x. Take half its coefficient (3.6875). Square it (13.59765625) and add it to both sides. Add '13.59765625' to each side of the equation. 7.375x + 13.59765625 + x2 = -1.875 + 13.59765625 Reorder the terms: 13.59765625 + 7.375x + x2 = -1.875 + 13.59765625 Combine like terms: -1.875 + 13.59765625 = 11.72265625 13.59765625 + 7.375x + x2 = 11.72265625 Factor a perfect square on the left side: (x + 3.6875)(x + 3.6875) = 11.72265625 Calculate the square root of the right side: 3.423836481 Break this problem into two subproblems by setting (x + 3.6875) equal to 3.423836481 and -3.423836481.

Subproblem 1

x + 3.6875 = 3.423836481 Simplifying x + 3.6875 = 3.423836481 Reorder the terms: 3.6875 + x = 3.423836481 Solving 3.6875 + x = 3.423836481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6875' to each side of the equation. 3.6875 + -3.6875 + x = 3.423836481 + -3.6875 Combine like terms: 3.6875 + -3.6875 = 0.0000 0.0000 + x = 3.423836481 + -3.6875 x = 3.423836481 + -3.6875 Combine like terms: 3.423836481 + -3.6875 = -0.263663519 x = -0.263663519 Simplifying x = -0.263663519

Subproblem 2

x + 3.6875 = -3.423836481 Simplifying x + 3.6875 = -3.423836481 Reorder the terms: 3.6875 + x = -3.423836481 Solving 3.6875 + x = -3.423836481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6875' to each side of the equation. 3.6875 + -3.6875 + x = -3.423836481 + -3.6875 Combine like terms: 3.6875 + -3.6875 = 0.0000 0.0000 + x = -3.423836481 + -3.6875 x = -3.423836481 + -3.6875 Combine like terms: -3.423836481 + -3.6875 = -7.111336481 x = -7.111336481 Simplifying x = -7.111336481

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.263663519, -7.111336481}

Solution

x = {-0.263663519, -7.111336481}

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