10x-4x(x-3)=6x+4

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Solution for 10x-4x(x-3)=6x+4 equation:


Simplifying
10x + -4x(x + -3) = 6x + 4

Reorder the terms:
10x + -4x(-3 + x) = 6x + 4
10x + (-3 * -4x + x * -4x) = 6x + 4
10x + (12x + -4x2) = 6x + 4

Combine like terms: 10x + 12x = 22x
22x + -4x2 = 6x + 4

Reorder the terms:
22x + -4x2 = 4 + 6x

Solving
22x + -4x2 = 4 + 6x

Solving for variable 'x'.

Reorder the terms:
-4 + 22x + -6x + -4x2 = 4 + 6x + -4 + -6x

Combine like terms: 22x + -6x = 16x
-4 + 16x + -4x2 = 4 + 6x + -4 + -6x

Reorder the terms:
-4 + 16x + -4x2 = 4 + -4 + 6x + -6x

Combine like terms: 4 + -4 = 0
-4 + 16x + -4x2 = 0 + 6x + -6x
-4 + 16x + -4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-4 + 16x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 4x + -1x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-1 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying -1 + 4x + -1x2 = 0 Solving -1 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -4x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -4x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x + x2 = 0 + -1 -4x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4x + x2 = -1 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -1 + 4 Reorder the terms: 4 + -4x + x2 = -1 + 4 Combine like terms: -1 + 4 = 3 4 + -4x + x2 = 3 Factor a perfect square on the left side: (x + -2)(x + -2) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + -2) equal to 1.732050808 and -1.732050808.

Subproblem 1

x + -2 = 1.732050808 Simplifying x + -2 = 1.732050808 Reorder the terms: -2 + x = 1.732050808 Solving -2 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.732050808 + 2 x = 1.732050808 + 2 Combine like terms: 1.732050808 + 2 = 3.732050808 x = 3.732050808 Simplifying x = 3.732050808

Subproblem 2

x + -2 = -1.732050808 Simplifying x + -2 = -1.732050808 Reorder the terms: -2 + x = -1.732050808 Solving -2 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.732050808 + 2 x = -1.732050808 + 2 Combine like terms: -1.732050808 + 2 = 0.267949192 x = 0.267949192 Simplifying x = 0.267949192

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.732050808, 0.267949192}

Solution

x = {3.732050808, 0.267949192}

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