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Simplifying x2 + 0.08x = 216 Reorder the terms: 0.08x + x2 = 216 Solving 0.08x + x2 = 216 Solving for variable 'x'. Reorder the terms: -216 + 0.08x + x2 = 216 + -216 Combine like terms: 216 + -216 = 0 -216 + 0.08x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '216' to each side of the equation. -216 + 0.08x + 216 + x2 = 0 + 216 Reorder the terms: -216 + 216 + 0.08x + x2 = 0 + 216 Combine like terms: -216 + 216 = 0 0 + 0.08x + x2 = 0 + 216 0.08x + x2 = 0 + 216 Combine like terms: 0 + 216 = 216 0.08x + x2 = 216 The x term is 0.08x. Take half its coefficient (0.04). Square it (0.0016) and add it to both sides. Add '0.0016' to each side of the equation. 0.08x + 0.0016 + x2 = 216 + 0.0016 Reorder the terms: 0.0016 + 0.08x + x2 = 216 + 0.0016 Combine like terms: 216 + 0.0016 = 216.0016 0.0016 + 0.08x + x2 = 216.0016 Factor a perfect square on the left side: (x + 0.04)(x + 0.04) = 216.0016 Calculate the square root of the right side: 14.69699289 Break this problem into two subproblems by setting (x + 0.04) equal to 14.69699289 and -14.69699289.Subproblem 1
x + 0.04 = 14.69699289 Simplifying x + 0.04 = 14.69699289 Reorder the terms: 0.04 + x = 14.69699289 Solving 0.04 + x = 14.69699289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04' to each side of the equation. 0.04 + -0.04 + x = 14.69699289 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + x = 14.69699289 + -0.04 x = 14.69699289 + -0.04 Combine like terms: 14.69699289 + -0.04 = 14.65699289 x = 14.65699289 Simplifying x = 14.65699289Subproblem 2
x + 0.04 = -14.69699289 Simplifying x + 0.04 = -14.69699289 Reorder the terms: 0.04 + x = -14.69699289 Solving 0.04 + x = -14.69699289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04' to each side of the equation. 0.04 + -0.04 + x = -14.69699289 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + x = -14.69699289 + -0.04 x = -14.69699289 + -0.04 Combine like terms: -14.69699289 + -0.04 = -14.73699289 x = -14.73699289 Simplifying x = -14.73699289Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.65699289, -14.73699289}
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