12x(x-20)=-48

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Solution for 12x(x-20)=-48 equation:


Simplifying
12x(x + -20) = -48

Reorder the terms:
12x(-20 + x) = -48
(-20 * 12x + x * 12x) = -48
(-240x + 12x2) = -48

Solving
-240x + 12x2 = -48

Solving for variable 'x'.

Reorder the terms:
48 + -240x + 12x2 = -48 + 48

Combine like terms: -48 + 48 = 0
48 + -240x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(4 + -20x + x2) = 0

Ignore the factor 12.

Subproblem 1

Set the factor '(4 + -20x + x2)' equal to zero and attempt to solve: Simplifying 4 + -20x + x2 = 0 Solving 4 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -20x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -20x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -20x + x2 = 0 + -4 -20x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -20x + x2 = -4 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 = -4 + 100 Reorder the terms: 100 + -20x + x2 = -4 + 100 Combine like terms: -4 + 100 = 96 100 + -20x + x2 = 96 Factor a perfect square on the left side: (x + -10)(x + -10) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + -10) equal to 9.797958971 and -9.797958971.

Subproblem 1

x + -10 = 9.797958971 Simplifying x + -10 = 9.797958971 Reorder the terms: -10 + x = 9.797958971 Solving -10 + x = 9.797958971 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 = 9.797958971 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.797958971 + 10 x = 9.797958971 + 10 Combine like terms: 9.797958971 + 10 = 19.797958971 x = 19.797958971 Simplifying x = 19.797958971

Subproblem 2

x + -10 = -9.797958971 Simplifying x + -10 = -9.797958971 Reorder the terms: -10 + x = -9.797958971 Solving -10 + x = -9.797958971 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 = -9.797958971 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.797958971 + 10 x = -9.797958971 + 10 Combine like terms: -9.797958971 + 10 = 0.202041029 x = 0.202041029 Simplifying x = 0.202041029

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.797958971, 0.202041029}

Solution

x = {19.797958971, 0.202041029}

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