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Simplifying 0 = 0.0006x2 + 0.036x + -0.36 Reorder the terms: 0 = -0.36 + 0.036x + 0.0006x2 Solving 0 = -0.36 + 0.036x + 0.0006x2 Solving for variable 'x'. Combine like terms: 0 + 0.36 = 0.36 0.36 + -0.036x + -0.0006x2 = -0.36 + 0.036x + 0.0006x2 + 0.36 + -0.036x + -0.0006x2 Reorder the terms: 0.36 + -0.036x + -0.0006x2 = -0.36 + 0.36 + 0.036x + -0.036x + 0.0006x2 + -0.0006x2 Combine like terms: -0.36 + 0.36 = 0.00 0.36 + -0.036x + -0.0006x2 = 0.00 + 0.036x + -0.036x + 0.0006x2 + -0.0006x2 0.36 + -0.036x + -0.0006x2 = 0.036x + -0.036x + 0.0006x2 + -0.0006x2 Combine like terms: 0.036x + -0.036x = 0.000 0.36 + -0.036x + -0.0006x2 = 0.000 + 0.0006x2 + -0.0006x2 0.36 + -0.036x + -0.0006x2 = 0.0006x2 + -0.0006x2 Combine like terms: 0.0006x2 + -0.0006x2 = 0.0000 0.36 + -0.036x + -0.0006x2 = 0.0000 Begin completing the square. Divide all terms by -0.0006 the coefficient of the squared term: Divide each side by '-0.0006'. -600 + 60x + x2 = 0 Move the constant term to the right: Add '600' to each side of the equation. -600 + 60x + 600 + x2 = 0 + 600 Reorder the terms: -600 + 600 + 60x + x2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + 60x + x2 = 0 + 600 60x + x2 = 0 + 600 Combine like terms: 0 + 600 = 600 60x + x2 = 600 The x term is 60x. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60x + 900 + x2 = 600 + 900 Reorder the terms: 900 + 60x + x2 = 600 + 900 Combine like terms: 600 + 900 = 1500 900 + 60x + x2 = 1500 Factor a perfect square on the left side: (x + 30)(x + 30) = 1500 Calculate the square root of the right side: 38.729833462 Break this problem into two subproblems by setting (x + 30) equal to 38.729833462 and -38.729833462.Subproblem 1
x + 30 = 38.729833462 Simplifying x + 30 = 38.729833462 Reorder the terms: 30 + x = 38.729833462 Solving 30 + x = 38.729833462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 38.729833462 + -30 Combine like terms: 30 + -30 = 0 0 + x = 38.729833462 + -30 x = 38.729833462 + -30 Combine like terms: 38.729833462 + -30 = 8.729833462 x = 8.729833462 Simplifying x = 8.729833462Subproblem 2
x + 30 = -38.729833462 Simplifying x + 30 = -38.729833462 Reorder the terms: 30 + x = -38.729833462 Solving 30 + x = -38.729833462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = -38.729833462 + -30 Combine like terms: 30 + -30 = 0 0 + x = -38.729833462 + -30 x = -38.729833462 + -30 Combine like terms: -38.729833462 + -30 = -68.729833462 x = -68.729833462 Simplifying x = -68.729833462Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.729833462, -68.729833462}
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