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Simplifying 0 = 0.17x + -1(1.9 + 0.15x + -0.0001x2) 0 = 0.17x + (1.9 * -1 + 0.15x * -1 + -0.0001x2 * -1) 0 = 0.17x + (-1.9 + -0.15x + 0.0001x2) Reorder the terms: 0 = -1.9 + 0.17x + -0.15x + 0.0001x2 Combine like terms: 0.17x + -0.15x = 0.02x 0 = -1.9 + 0.02x + 0.0001x2 Solving 0 = -1.9 + 0.02x + 0.0001x2 Solving for variable 'x'. Combine like terms: 0 + 1.9 = 1.9 1.9 + -0.02x + -0.0001x2 = -1.9 + 0.02x + 0.0001x2 + 1.9 + -0.02x + -0.0001x2 Reorder the terms: 1.9 + -0.02x + -0.0001x2 = -1.9 + 1.9 + 0.02x + -0.02x + 0.0001x2 + -0.0001x2 Combine like terms: -1.9 + 1.9 = 0.0 1.9 + -0.02x + -0.0001x2 = 0.0 + 0.02x + -0.02x + 0.0001x2 + -0.0001x2 1.9 + -0.02x + -0.0001x2 = 0.02x + -0.02x + 0.0001x2 + -0.0001x2 Combine like terms: 0.02x + -0.02x = 0.00 1.9 + -0.02x + -0.0001x2 = 0.00 + 0.0001x2 + -0.0001x2 1.9 + -0.02x + -0.0001x2 = 0.0001x2 + -0.0001x2 Combine like terms: 0.0001x2 + -0.0001x2 = 0.0000 1.9 + -0.02x + -0.0001x2 = 0.0000 Begin completing the square. Divide all terms by -0.0001 the coefficient of the squared term: Divide each side by '-0.0001'. -19000 + 200x + x2 = 0 Move the constant term to the right: Add '19000' to each side of the equation. -19000 + 200x + 19000 + x2 = 0 + 19000 Reorder the terms: -19000 + 19000 + 200x + x2 = 0 + 19000 Combine like terms: -19000 + 19000 = 0 0 + 200x + x2 = 0 + 19000 200x + x2 = 0 + 19000 Combine like terms: 0 + 19000 = 19000 200x + x2 = 19000 The x term is 200x. Take half its coefficient (100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. 200x + 10000 + x2 = 19000 + 10000 Reorder the terms: 10000 + 200x + x2 = 19000 + 10000 Combine like terms: 19000 + 10000 = 29000 10000 + 200x + x2 = 29000 Factor a perfect square on the left side: (x + 100)(x + 100) = 29000 Calculate the square root of the right side: 170.293863659 Break this problem into two subproblems by setting (x + 100) equal to 170.293863659 and -170.293863659.Subproblem 1
x + 100 = 170.293863659 Simplifying x + 100 = 170.293863659 Reorder the terms: 100 + x = 170.293863659 Solving 100 + x = 170.293863659 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = 170.293863659 + -100 Combine like terms: 100 + -100 = 0 0 + x = 170.293863659 + -100 x = 170.293863659 + -100 Combine like terms: 170.293863659 + -100 = 70.293863659 x = 70.293863659 Simplifying x = 70.293863659Subproblem 2
x + 100 = -170.293863659 Simplifying x + 100 = -170.293863659 Reorder the terms: 100 + x = -170.293863659 Solving 100 + x = -170.293863659 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = -170.293863659 + -100 Combine like terms: 100 + -100 = 0 0 + x = -170.293863659 + -100 x = -170.293863659 + -100 Combine like terms: -170.293863659 + -100 = -270.293863659 x = -270.293863659 Simplifying x = -270.293863659Solution
The solution to the problem is based on the solutions from the subproblems. x = {70.293863659, -270.293863659}
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