0=20x-2x^2-4-2x^2

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Solution for 0=20x-2x^2-4-2x^2 equation:


Simplifying
0 = 20x + -2x2 + -4 + -2x2

Reorder the terms:
0 = -4 + 20x + -2x2 + -2x2

Combine like terms: -2x2 + -2x2 = -4x2
0 = -4 + 20x + -4x2

Solving
0 = -4 + 20x + -4x2

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -5x + x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(1 + -5x + x2)' equal to zero and attempt to solve: Simplifying 1 + -5x + x2 = 0 Solving 1 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x + x2 = 0 + -1 -5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -5x + x2 = -1 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -1 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -1 + 6.25 Combine like terms: -1 + 6.25 = 5.25 6.25 + -5x + x2 = 5.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + -2.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

x + -2.5 = 2.291287847 Simplifying x + -2.5 = 2.291287847 Reorder the terms: -2.5 + x = 2.291287847 Solving -2.5 + x = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.291287847 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.291287847 + 2.5 x = 2.291287847 + 2.5 Combine like terms: 2.291287847 + 2.5 = 4.791287847 x = 4.791287847 Simplifying x = 4.791287847

Subproblem 2

x + -2.5 = -2.291287847 Simplifying x + -2.5 = -2.291287847 Reorder the terms: -2.5 + x = -2.291287847 Solving -2.5 + x = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.291287847 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.291287847 + 2.5 x = -2.291287847 + 2.5 Combine like terms: -2.291287847 + 2.5 = 0.208712153 x = 0.208712153 Simplifying x = 0.208712153

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.791287847, 0.208712153}

Solution

x = {4.791287847, 0.208712153}

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