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Simplifying x(x + 0.15) = 0.0000000084 Reorder the terms: x(0.15 + x) = 0.0000000084 (0.15 * x + x * x) = 0.0000000084 (0.15x + x2) = 0.0000000084 Solving 0.15x + x2 = 0.0000000084 Solving for variable 'x'. Reorder the terms: -0.0000000084 + 0.15x + x2 = 0.0000000084 + -0.0000000084 Combine like terms: 0.0000000084 + -0.0000000084 = 0.0000000000 -0.0000000084 + 0.15x + x2 = 0.0000000000 Begin completing the square. Move the constant term to the right: Add '0.0000000084' to each side of the equation. -0.0000000084 + 0.15x + 0.0000000084 + x2 = 0.0000000000 + 0.0000000084 Reorder the terms: -0.0000000084 + 0.0000000084 + 0.15x + x2 = 0.0000000000 + 0.0000000084 Combine like terms: -0.0000000084 + 0.0000000084 = 0.0000000000 0.0000000000 + 0.15x + x2 = 0.0000000000 + 0.0000000084 0.15x + x2 = 0.0000000000 + 0.0000000084 Combine like terms: 0.0000000000 + 0.0000000084 = 0.0000000084 0.15x + x2 = 0.0000000084 The x term is 0.15x. Take half its coefficient (0.075). Square it (0.005625) and add it to both sides. Add '0.005625' to each side of the equation. 0.15x + 0.005625 + x2 = 0.0000000084 + 0.005625 Reorder the terms: 0.005625 + 0.15x + x2 = 0.0000000084 + 0.005625 Combine like terms: 0.0000000084 + 0.005625 = 0.0056250084 0.005625 + 0.15x + x2 = 0.0056250084 Factor a perfect square on the left side: (x + 0.075)(x + 0.075) = 0.0056250084 Calculate the square root of the right side: 0.075000056 Break this problem into two subproblems by setting (x + 0.075) equal to 0.075000056 and -0.075000056.Subproblem 1
x + 0.075 = 0.075000056 Simplifying x + 0.075 = 0.075000056 Reorder the terms: 0.075 + x = 0.075000056 Solving 0.075 + x = 0.075000056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = 0.075000056 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = 0.075000056 + -0.075 x = 0.075000056 + -0.075 Combine like terms: 0.075000056 + -0.075 = 0.000000056 x = 0.000000056 Simplifying x = 0.000000056Subproblem 2
x + 0.075 = -0.075000056 Simplifying x + 0.075 = -0.075000056 Reorder the terms: 0.075 + x = -0.075000056 Solving 0.075 + x = -0.075000056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = -0.075000056 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = -0.075000056 + -0.075 x = -0.075000056 + -0.075 Combine like terms: -0.075000056 + -0.075 = -0.150000056 x = -0.150000056 Simplifying x = -0.150000056Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000000056, -0.150000056}
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