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Simplifying 30x2 + 1000x + -80000 = 0 Reorder the terms: -80000 + 1000x + 30x2 = 0 Solving -80000 + 1000x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(-8000 + 100x + 3x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-8000 + 100x + 3x2)' equal to zero and attempt to solve: Simplifying -8000 + 100x + 3x2 = 0 Solving -8000 + 100x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2666.666667 + 33.33333333x + x2 = 0 Move the constant term to the right: Add '2666.666667' to each side of the equation. -2666.666667 + 33.33333333x + 2666.666667 + x2 = 0 + 2666.666667 Reorder the terms: -2666.666667 + 2666.666667 + 33.33333333x + x2 = 0 + 2666.666667 Combine like terms: -2666.666667 + 2666.666667 = 0.000000 0.000000 + 33.33333333x + x2 = 0 + 2666.666667 33.33333333x + x2 = 0 + 2666.666667 Combine like terms: 0 + 2666.666667 = 2666.666667 33.33333333x + x2 = 2666.666667 The x term is 33.33333333x. Take half its coefficient (16.66666667). Square it (277.7777779) and add it to both sides. Add '277.7777779' to each side of the equation. 33.33333333x + 277.7777779 + x2 = 2666.666667 + 277.7777779 Reorder the terms: 277.7777779 + 33.33333333x + x2 = 2666.666667 + 277.7777779 Combine like terms: 2666.666667 + 277.7777779 = 2944.4444449 277.7777779 + 33.33333333x + x2 = 2944.4444449 Factor a perfect square on the left side: (x + 16.66666667)(x + 16.66666667) = 2944.4444449 Calculate the square root of the right side: 54.262735325 Break this problem into two subproblems by setting (x + 16.66666667) equal to 54.262735325 and -54.262735325.Subproblem 1
x + 16.66666667 = 54.262735325 Simplifying x + 16.66666667 = 54.262735325 Reorder the terms: 16.66666667 + x = 54.262735325 Solving 16.66666667 + x = 54.262735325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.66666667' to each side of the equation. 16.66666667 + -16.66666667 + x = 54.262735325 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + x = 54.262735325 + -16.66666667 x = 54.262735325 + -16.66666667 Combine like terms: 54.262735325 + -16.66666667 = 37.596068655 x = 37.596068655 Simplifying x = 37.596068655Subproblem 2
x + 16.66666667 = -54.262735325 Simplifying x + 16.66666667 = -54.262735325 Reorder the terms: 16.66666667 + x = -54.262735325 Solving 16.66666667 + x = -54.262735325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.66666667' to each side of the equation. 16.66666667 + -16.66666667 + x = -54.262735325 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + x = -54.262735325 + -16.66666667 x = -54.262735325 + -16.66666667 Combine like terms: -54.262735325 + -16.66666667 = -70.929401995 x = -70.929401995 Simplifying x = -70.929401995Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.596068655, -70.929401995}Solution
x = {37.596068655, -70.929401995}
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