20=(12x^2)-32x

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Solution for 20=(12x^2)-32x equation:


Simplifying
20 = (12x2) + -32x

Reorder the terms:
20 = -32x + (12x2)

Solving
20 = -32x + (12x2)

Solving for variable 'x'.

Reorder the terms:
20 + 32x + (-12x2) = -32x + 32x + (12x2) + (-12x2)

Combine like terms: -32x + 32x = 0
20 + 32x + (-12x2) = 0 + (12x2) + (-12x2)
20 + 32x + (-12x2) = (12x2) + (-12x2)

Combine like terms: (12x2) + (-12x2) = 0
20 + 32x + (-12x2) = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + 8x + (-3x2)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(5 + 8x + (-3x2))' equal to zero and attempt to solve: Simplifying 5 + 8x + (-3x2) = 0 Solving 5 + 8x + (-3x2) = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1.666666667 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -2.666666667x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -2.666666667x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -2.666666667x + x2 = 0 + 1.666666667 -2.666666667x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -2.666666667x + x2 = 1.666666667 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = 1.666666667 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 1.666666667 + 1.777777780 Combine like terms: 1.666666667 + 1.777777780 = 3.444444447 1.777777780 + -2.666666667x + x2 = 3.444444447 Factor a perfect square on the left side: ((x) + -1.333333334)((x) + -1.333333334) = 3.444444447 Calculate the square root of the right side: 1.855921455 Break this problem into two subproblems by setting ((x) + -1.333333334) equal to 1.855921455 and -1.855921455.

Subproblem 1

(x) + -1.333333334 = 1.855921455 Simplifying (x) + -1.333333334 = 1.855921455 x + -1.333333334 = 1.855921455 Reorder the terms: -1.333333334 + x = 1.855921455 Solving -1.333333334 + x = 1.855921455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 1.855921455 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.855921455 + 1.333333334 x = 1.855921455 + 1.333333334 Combine like terms: 1.855921455 + 1.333333334 = 3.189254789 x = 3.189254789 Simplifying x = 3.189254789

Subproblem 2

(x) + -1.333333334 = -1.855921455 Simplifying (x) + -1.333333334 = -1.855921455 x + -1.333333334 = -1.855921455 Reorder the terms: -1.333333334 + x = -1.855921455 Solving -1.333333334 + x = -1.855921455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -1.855921455 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.855921455 + 1.333333334 x = -1.855921455 + 1.333333334 Combine like terms: -1.855921455 + 1.333333334 = -0.522588121 x = -0.522588121 Simplifying x = -0.522588121

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.189254789, -0.522588121}

Solution

x = {3.189254789, -0.522588121}

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