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Simplifying 15x2 + x + -0.09 = 0 Reorder the terms: -0.09 + x + 15x2 = 0 Solving -0.09 + x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.006 + 0.06666666667x + x2 = 0 Move the constant term to the right: Add '0.006' to each side of the equation. -0.006 + 0.06666666667x + 0.006 + x2 = 0 + 0.006 Reorder the terms: -0.006 + 0.006 + 0.06666666667x + x2 = 0 + 0.006 Combine like terms: -0.006 + 0.006 = 0.000 0.000 + 0.06666666667x + x2 = 0 + 0.006 0.06666666667x + x2 = 0 + 0.006 Combine like terms: 0 + 0.006 = 0.006 0.06666666667x + x2 = 0.006 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. 0.06666666667x + 0.25 + x2 = 0.006 + 0.25 Reorder the terms: 0.25 + 0.06666666667x + x2 = 0.006 + 0.25 Combine like terms: 0.006 + 0.25 = 0.256 0.25 + 0.06666666667x + x2 = 0.256 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.256 Calculate the square root of the right side: 0.505964426 Break this problem into two subproblems by setting (x + 0.5) equal to 0.505964426 and -0.505964426.Subproblem 1
x + 0.5 = 0.505964426 Simplifying x + 0.5 = 0.505964426 Reorder the terms: 0.5 + x = 0.505964426 Solving 0.5 + x = 0.505964426 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 = 0.505964426 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.505964426 + -0.5 x = 0.505964426 + -0.5 Combine like terms: 0.505964426 + -0.5 = 0.005964426 x = 0.005964426 Simplifying x = 0.005964426Subproblem 2
x + 0.5 = -0.505964426 Simplifying x + 0.5 = -0.505964426 Reorder the terms: 0.5 + x = -0.505964426 Solving 0.5 + x = -0.505964426 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 = -0.505964426 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.505964426 + -0.5 x = -0.505964426 + -0.5 Combine like terms: -0.505964426 + -0.5 = -1.005964426 x = -1.005964426 Simplifying x = -1.005964426Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.005964426, -1.005964426}
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