=12x^2-240x+800

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Solution for =12x^2-240x+800 equation:


Simplifying
0 = 12x2 + -240x + 800

Reorder the terms:
0 = 800 + -240x + 12x2

Solving
0 = 800 + -240x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + -800 = -800
-800 + 240x + -12x2 = 800 + -240x + 12x2 + -800 + 240x + -12x2

Reorder the terms:
-800 + 240x + -12x2 = 800 + -800 + -240x + 240x + 12x2 + -12x2

Combine like terms: 800 + -800 = 0
-800 + 240x + -12x2 = 0 + -240x + 240x + 12x2 + -12x2
-800 + 240x + -12x2 = -240x + 240x + 12x2 + -12x2

Combine like terms: -240x + 240x = 0
-800 + 240x + -12x2 = 0 + 12x2 + -12x2
-800 + 240x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-800 + 240x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-200 + 60x + -3x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-200 + 60x + -3x2)' equal to zero and attempt to solve: Simplifying -200 + 60x + -3x2 = 0 Solving -200 + 60x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 66.66666667 + -20x + x2 = 0 Move the constant term to the right: Add '-66.66666667' to each side of the equation. 66.66666667 + -20x + -66.66666667 + x2 = 0 + -66.66666667 Reorder the terms: 66.66666667 + -66.66666667 + -20x + x2 = 0 + -66.66666667 Combine like terms: 66.66666667 + -66.66666667 = 0.00000000 0.00000000 + -20x + x2 = 0 + -66.66666667 -20x + x2 = 0 + -66.66666667 Combine like terms: 0 + -66.66666667 = -66.66666667 -20x + x2 = -66.66666667 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -66.66666667 + 100 Reorder the terms: 100 + -20x + x2 = -66.66666667 + 100 Combine like terms: -66.66666667 + 100 = 33.33333333 100 + -20x + x2 = 33.33333333 Factor a perfect square on the left side: (x + -10)(x + -10) = 33.33333333 Calculate the square root of the right side: 5.773502692 Break this problem into two subproblems by setting (x + -10) equal to 5.773502692 and -5.773502692.

Subproblem 1

x + -10 = 5.773502692 Simplifying x + -10 = 5.773502692 Reorder the terms: -10 + x = 5.773502692 Solving -10 + x = 5.773502692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 5.773502692 + 10 Combine like terms: -10 + 10 = 0 0 + x = 5.773502692 + 10 x = 5.773502692 + 10 Combine like terms: 5.773502692 + 10 = 15.773502692 x = 15.773502692 Simplifying x = 15.773502692

Subproblem 2

x + -10 = -5.773502692 Simplifying x + -10 = -5.773502692 Reorder the terms: -10 + x = -5.773502692 Solving -10 + x = -5.773502692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -5.773502692 + 10 Combine like terms: -10 + 10 = 0 0 + x = -5.773502692 + 10 x = -5.773502692 + 10 Combine like terms: -5.773502692 + 10 = 4.226497308 x = 4.226497308 Simplifying x = 4.226497308

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.773502692, 4.226497308}

Solution

x = {15.773502692, 4.226497308}

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