4(x-1)9x=22

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Solution for 4(x-1)9x=22 equation:


Simplifying
4(x + -1) * 9x = 22

Reorder the terms:
4(-1 + x) * 9x = 22

Reorder the terms for easier multiplication:
4 * 9x(-1 + x) = 22

Multiply 4 * 9
36x(-1 + x) = 22
(-1 * 36x + x * 36x) = 22
(-36x + 36x2) = 22

Solving
-36x + 36x2 = 22

Solving for variable 'x'.

Reorder the terms:
-22 + -36x + 36x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-22 + -36x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + -18x + 18x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-11 + -18x + 18x2)' equal to zero and attempt to solve: Simplifying -11 + -18x + 18x2 = 0 Solving -11 + -18x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.6111111111 + -1x + x2 = 0 Move the constant term to the right: Add '0.6111111111' to each side of the equation. -0.6111111111 + -1x + 0.6111111111 + x2 = 0 + 0.6111111111 Reorder the terms: -0.6111111111 + 0.6111111111 + -1x + x2 = 0 + 0.6111111111 Combine like terms: -0.6111111111 + 0.6111111111 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + 0.6111111111 -1x + x2 = 0 + 0.6111111111 Combine like terms: 0 + 0.6111111111 = 0.6111111111 -1x + x2 = 0.6111111111 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.6111111111 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.6111111111 + 0.25 Combine like terms: 0.6111111111 + 0.25 = 0.8611111111 0.25 + -1x + x2 = 0.8611111111 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.8611111111 Calculate the square root of the right side: 0.927960727 Break this problem into two subproblems by setting (x + -0.5) equal to 0.927960727 and -0.927960727.

Subproblem 1

x + -0.5 = 0.927960727 Simplifying x + -0.5 = 0.927960727 Reorder the terms: -0.5 + x = 0.927960727 Solving -0.5 + x = 0.927960727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.927960727 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.927960727 + 0.5 x = 0.927960727 + 0.5 Combine like terms: 0.927960727 + 0.5 = 1.427960727 x = 1.427960727 Simplifying x = 1.427960727

Subproblem 2

x + -0.5 = -0.927960727 Simplifying x + -0.5 = -0.927960727 Reorder the terms: -0.5 + x = -0.927960727 Solving -0.5 + x = -0.927960727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.927960727 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.927960727 + 0.5 x = -0.927960727 + 0.5 Combine like terms: -0.927960727 + 0.5 = -0.427960727 x = -0.427960727 Simplifying x = -0.427960727

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.427960727, -0.427960727}

Solution

x = {1.427960727, -0.427960727}

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