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Simplifying (1.5x2) + 120x + -4000 = 0 Reorder the terms: -4000 + 120x + (1.5x2) = 0 Solving -4000 + 120x + (1.5x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. -2666.666667 + 80x + x2 = 0 Move the constant term to the right: Add '2666.666667' to each side of the equation. -2666.666667 + 80x + 2666.666667 + x2 = 0 + 2666.666667 Reorder the terms: -2666.666667 + 2666.666667 + 80x + x2 = 0 + 2666.666667 Combine like terms: -2666.666667 + 2666.666667 = 0.000000 0.000000 + 80x + x2 = 0 + 2666.666667 80x + x2 = 0 + 2666.666667 Combine like terms: 0 + 2666.666667 = 2666.666667 80x + x2 = 2666.666667 The x term is 80x. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80x + 1600 + x2 = 2666.666667 + 1600 Reorder the terms: 1600 + 80x + x2 = 2666.666667 + 1600 Combine like terms: 2666.666667 + 1600 = 4266.666667 1600 + 80x + x2 = 4266.666667 Factor a perfect square on the left side: ((x) + 40)((x) + 40) = 4266.666667 Calculate the square root of the right side: 65.319726477 Break this problem into two subproblems by setting ((x) + 40) equal to 65.319726477 and -65.319726477.Subproblem 1
(x) + 40 = 65.319726477 Simplifying (x) + 40 = 65.319726477 x + 40 = 65.319726477 Reorder the terms: 40 + x = 65.319726477 Solving 40 + x = 65.319726477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = 65.319726477 + -40 Combine like terms: 40 + -40 = 0 0 + x = 65.319726477 + -40 x = 65.319726477 + -40 Combine like terms: 65.319726477 + -40 = 25.319726477 x = 25.319726477 Simplifying x = 25.319726477Subproblem 2
(x) + 40 = -65.319726477 Simplifying (x) + 40 = -65.319726477 x + 40 = -65.319726477 Reorder the terms: 40 + x = -65.319726477 Solving 40 + x = -65.319726477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = -65.319726477 + -40 Combine like terms: 40 + -40 = 0 0 + x = -65.319726477 + -40 x = -65.319726477 + -40 Combine like terms: -65.319726477 + -40 = -105.319726477 x = -105.319726477 Simplifying x = -105.319726477Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.319726477, -105.319726477}
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