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Simplifying 1.5x2 + x + 20000 = 120000 Reorder the terms: 20000 + x + 1.5x2 = 120000 Solving 20000 + x + 1.5x2 = 120000 Solving for variable 'x'. Reorder the terms: 20000 + -120000 + x + 1.5x2 = 120000 + -120000 Combine like terms: 20000 + -120000 = -100000 -100000 + x + 1.5x2 = 120000 + -120000 Combine like terms: 120000 + -120000 = 0 -100000 + x + 1.5x2 = 0 Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. -66666.66667 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '66666.66667' to each side of the equation. -66666.66667 + 0.6666666667x + 66666.66667 + x2 = 0 + 66666.66667 Reorder the terms: -66666.66667 + 66666.66667 + 0.6666666667x + x2 = 0 + 66666.66667 Combine like terms: -66666.66667 + 66666.66667 = 0.00000 0.00000 + 0.6666666667x + x2 = 0 + 66666.66667 0.6666666667x + x2 = 0 + 66666.66667 Combine like terms: 0 + 66666.66667 = 66666.66667 0.6666666667x + x2 = 66666.66667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.6666666667x + 0.25 + x2 = 66666.66667 + 0.25 Reorder the terms: 0.25 + 0.6666666667x + x2 = 66666.66667 + 0.25 Combine like terms: 66666.66667 + 0.25 = 66666.91667 0.25 + 0.6666666667x + x2 = 66666.91667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 66666.91667 Calculate the square root of the right side: 258.199373876 Break this problem into two subproblems by setting (x + 0.5) equal to 258.199373876 and -258.199373876.Subproblem 1
x + 0.5 = 258.199373876 Simplifying x + 0.5 = 258.199373876 Reorder the terms: 0.5 + x = 258.199373876 Solving 0.5 + x = 258.199373876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 258.199373876 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 258.199373876 + -0.5 x = 258.199373876 + -0.5 Combine like terms: 258.199373876 + -0.5 = 257.699373876 x = 257.699373876 Simplifying x = 257.699373876Subproblem 2
x + 0.5 = -258.199373876 Simplifying x + 0.5 = -258.199373876 Reorder the terms: 0.5 + x = -258.199373876 Solving 0.5 + x = -258.199373876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -258.199373876 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -258.199373876 + -0.5 x = -258.199373876 + -0.5 Combine like terms: -258.199373876 + -0.5 = -258.699373876 x = -258.699373876 Simplifying x = -258.699373876Solution
The solution to the problem is based on the solutions from the subproblems. x = {257.699373876, -258.699373876}
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