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Simplifying 24000 = x2 + 0.15x Reorder the terms: 24000 = 0.15x + x2 Solving 24000 = 0.15x + x2 Solving for variable 'x'. Reorder the terms: 24000 + -0.15x + -1x2 = 0.15x + -0.15x + x2 + -1x2 Combine like terms: 0.15x + -0.15x = 0.00 24000 + -0.15x + -1x2 = 0.00 + x2 + -1x2 24000 + -0.15x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 24000 + -0.15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24000 + 0.15x + x2 = 0 Move the constant term to the right: Add '24000' to each side of the equation. -24000 + 0.15x + 24000 + x2 = 0 + 24000 Reorder the terms: -24000 + 24000 + 0.15x + x2 = 0 + 24000 Combine like terms: -24000 + 24000 = 0 0 + 0.15x + x2 = 0 + 24000 0.15x + x2 = 0 + 24000 Combine like terms: 0 + 24000 = 24000 0.15x + x2 = 24000 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 = 24000 + 0.005625 Reorder the terms: 0.005625 + 0.15x + x2 = 24000 + 0.005625 Combine like terms: 24000 + 0.005625 = 24000.005625 0.005625 + 0.15x + x2 = 24000.005625 Factor a perfect square on the left side: (x + 0.075)(x + 0.075) = 24000.005625 Calculate the square root of the right side: 154.919352003 Break this problem into two subproblems by setting (x + 0.075) equal to 154.919352003 and -154.919352003.Subproblem 1
x + 0.075 = 154.919352003 Simplifying x + 0.075 = 154.919352003 Reorder the terms: 0.075 + x = 154.919352003 Solving 0.075 + x = 154.919352003 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 = 154.919352003 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = 154.919352003 + -0.075 x = 154.919352003 + -0.075 Combine like terms: 154.919352003 + -0.075 = 154.844352003 x = 154.844352003 Simplifying x = 154.844352003Subproblem 2
x + 0.075 = -154.919352003 Simplifying x + 0.075 = -154.919352003 Reorder the terms: 0.075 + x = -154.919352003 Solving 0.075 + x = -154.919352003 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 = -154.919352003 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = -154.919352003 + -0.075 x = -154.919352003 + -0.075 Combine like terms: -154.919352003 + -0.075 = -154.994352003 x = -154.994352003 Simplifying x = -154.994352003Solution
The solution to the problem is based on the solutions from the subproblems. x = {154.844352003, -154.994352003}
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