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Simplifying 15 + 0.4x + -0.05x2 = 0 Solving 15 + 0.4x + -0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -300 + -8x + x2 = 0 Move the constant term to the right: Add '300' to each side of the equation. -300 + -8x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + -8x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + -8x + x2 = 0 + 300 -8x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 -8x + x2 = 300 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 300 + 16 Reorder the terms: 16 + -8x + x2 = 300 + 16 Combine like terms: 300 + 16 = 316 16 + -8x + x2 = 316 Factor a perfect square on the left side: (x + -4)(x + -4) = 316 Calculate the square root of the right side: 17.776388835 Break this problem into two subproblems by setting (x + -4) equal to 17.776388835 and -17.776388835.Subproblem 1
x + -4 = 17.776388835 Simplifying x + -4 = 17.776388835 Reorder the terms: -4 + x = 17.776388835 Solving -4 + x = 17.776388835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 17.776388835 + 4 Combine like terms: -4 + 4 = 0 0 + x = 17.776388835 + 4 x = 17.776388835 + 4 Combine like terms: 17.776388835 + 4 = 21.776388835 x = 21.776388835 Simplifying x = 21.776388835Subproblem 2
x + -4 = -17.776388835 Simplifying x + -4 = -17.776388835 Reorder the terms: -4 + x = -17.776388835 Solving -4 + x = -17.776388835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -17.776388835 + 4 Combine like terms: -4 + 4 = 0 0 + x = -17.776388835 + 4 x = -17.776388835 + 4 Combine like terms: -17.776388835 + 4 = -13.776388835 x = -13.776388835 Simplifying x = -13.776388835Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.776388835, -13.776388835}
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