0=4x^2-8x-80

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Solution for 0=4x^2-8x-80 equation:


Simplifying
0 = 4x2 + -8x + -80

Reorder the terms:
0 = -80 + -8x + 4x2

Solving
0 = -80 + -8x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 80 = 80
80 + 8x + -4x2 = -80 + -8x + 4x2 + 80 + 8x + -4x2

Reorder the terms:
80 + 8x + -4x2 = -80 + 80 + -8x + 8x + 4x2 + -4x2

Combine like terms: -80 + 80 = 0
80 + 8x + -4x2 = 0 + -8x + 8x + 4x2 + -4x2
80 + 8x + -4x2 = -8x + 8x + 4x2 + -4x2

Combine like terms: -8x + 8x = 0
80 + 8x + -4x2 = 0 + 4x2 + -4x2
80 + 8x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
80 + 8x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(20 + 2x + -1x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(20 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying 20 + 2x + -1x2 = 0 Solving 20 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + -2x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -2x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -2x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -2x + x2 = 0 + 20 -2x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -2x + x2 = 20 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 20 + 1 Reorder the terms: 1 + -2x + x2 = 20 + 1 Combine like terms: 20 + 1 = 21 1 + -2x + x2 = 21 Factor a perfect square on the left side: (x + -1)(x + -1) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + -1) equal to 4.582575695 and -4.582575695.

Subproblem 1

x + -1 = 4.582575695 Simplifying x + -1 = 4.582575695 Reorder the terms: -1 + x = 4.582575695 Solving -1 + x = 4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 4.582575695 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.582575695 + 1 x = 4.582575695 + 1 Combine like terms: 4.582575695 + 1 = 5.582575695 x = 5.582575695 Simplifying x = 5.582575695

Subproblem 2

x + -1 = -4.582575695 Simplifying x + -1 = -4.582575695 Reorder the terms: -1 + x = -4.582575695 Solving -1 + x = -4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -4.582575695 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.582575695 + 1 x = -4.582575695 + 1 Combine like terms: -4.582575695 + 1 = -3.582575695 x = -3.582575695 Simplifying x = -3.582575695

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.582575695, -3.582575695}

Solution

x = {5.582575695, -3.582575695}

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