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Simplifying x2 + -0.3x = 200000 Reorder the terms: -0.3x + x2 = 200000 Solving -0.3x + x2 = 200000 Solving for variable 'x'. Reorder the terms: -200000 + -0.3x + x2 = 200000 + -200000 Combine like terms: 200000 + -200000 = 0 -200000 + -0.3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '200000' to each side of the equation. -200000 + -0.3x + 200000 + x2 = 0 + 200000 Reorder the terms: -200000 + 200000 + -0.3x + x2 = 0 + 200000 Combine like terms: -200000 + 200000 = 0 0 + -0.3x + x2 = 0 + 200000 -0.3x + x2 = 0 + 200000 Combine like terms: 0 + 200000 = 200000 -0.3x + x2 = 200000 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = 200000 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 200000 + 0.0225 Combine like terms: 200000 + 0.0225 = 200000.0225 0.0225 + -0.3x + x2 = 200000.0225 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 200000.0225 Calculate the square root of the right side: 447.213620656 Break this problem into two subproblems by setting (x + -0.15) equal to 447.213620656 and -447.213620656.Subproblem 1
x + -0.15 = 447.213620656 Simplifying x + -0.15 = 447.213620656 Reorder the terms: -0.15 + x = 447.213620656 Solving -0.15 + x = 447.213620656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 447.213620656 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 447.213620656 + 0.15 x = 447.213620656 + 0.15 Combine like terms: 447.213620656 + 0.15 = 447.363620656 x = 447.363620656 Simplifying x = 447.363620656Subproblem 2
x + -0.15 = -447.213620656 Simplifying x + -0.15 = -447.213620656 Reorder the terms: -0.15 + x = -447.213620656 Solving -0.15 + x = -447.213620656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -447.213620656 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -447.213620656 + 0.15 x = -447.213620656 + 0.15 Combine like terms: -447.213620656 + 0.15 = -447.063620656 x = -447.063620656 Simplifying x = -447.063620656Solution
The solution to the problem is based on the solutions from the subproblems. x = {447.363620656, -447.063620656}
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