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Simplifying x2 + -0.3 + 0.06x = 0 Reorder the terms: -0.3 + 0.06x + x2 = 0 Solving -0.3 + 0.06x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 0.06x + 0.3 + x2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + 0.06x + x2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 0.06x + x2 = 0 + 0.3 0.06x + x2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 0.06x + x2 = 0.3 The x term is 0.06x. Take half its coefficient (0.03). Square it (0.0009) and add it to both sides. Add '0.0009' to each side of the equation. 0.06x + 0.0009 + x2 = 0.3 + 0.0009 Reorder the terms: 0.0009 + 0.06x + x2 = 0.3 + 0.0009 Combine like terms: 0.3 + 0.0009 = 0.3009 0.0009 + 0.06x + x2 = 0.3009 Factor a perfect square on the left side: (x + 0.03)(x + 0.03) = 0.3009 Calculate the square root of the right side: 0.548543526 Break this problem into two subproblems by setting (x + 0.03) equal to 0.548543526 and -0.548543526.Subproblem 1
x + 0.03 = 0.548543526 Simplifying x + 0.03 = 0.548543526 Reorder the terms: 0.03 + x = 0.548543526 Solving 0.03 + x = 0.548543526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03' to each side of the equation. 0.03 + -0.03 + x = 0.548543526 + -0.03 Combine like terms: 0.03 + -0.03 = 0.00 0.00 + x = 0.548543526 + -0.03 x = 0.548543526 + -0.03 Combine like terms: 0.548543526 + -0.03 = 0.518543526 x = 0.518543526 Simplifying x = 0.518543526Subproblem 2
x + 0.03 = -0.548543526 Simplifying x + 0.03 = -0.548543526 Reorder the terms: 0.03 + x = -0.548543526 Solving 0.03 + x = -0.548543526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03' to each side of the equation. 0.03 + -0.03 + x = -0.548543526 + -0.03 Combine like terms: 0.03 + -0.03 = 0.00 0.00 + x = -0.548543526 + -0.03 x = -0.548543526 + -0.03 Combine like terms: -0.548543526 + -0.03 = -0.578543526 x = -0.578543526 Simplifying x = -0.578543526Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.518543526, -0.578543526}
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