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Simplifying 2x(0.5x + 6) = 1 Reorder the terms: 2x(6 + 0.5x) = 1 (6 * 2x + 0.5x * 2x) = 1 (12x + 1x2) = 1 Solving 12x + 1x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 12x + 1x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 12x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 12x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 12x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 12x + x2 = 0 + 1 12x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 12x + x2 = 1 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 1 + 36 Reorder the terms: 36 + 12x + x2 = 1 + 36 Combine like terms: 1 + 36 = 37 36 + 12x + x2 = 37 Factor a perfect square on the left side: (x + 6)(x + 6) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x + 6) equal to 6.08276253 and -6.08276253.Subproblem 1
x + 6 = 6.08276253 Simplifying x + 6 = 6.08276253 Reorder the terms: 6 + x = 6.08276253 Solving 6 + x = 6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 6.08276253 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.08276253 + -6 x = 6.08276253 + -6 Combine like terms: 6.08276253 + -6 = 0.08276253 x = 0.08276253 Simplifying x = 0.08276253Subproblem 2
x + 6 = -6.08276253 Simplifying x + 6 = -6.08276253 Reorder the terms: 6 + x = -6.08276253 Solving 6 + x = -6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -6.08276253 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.08276253 + -6 x = -6.08276253 + -6 Combine like terms: -6.08276253 + -6 = -12.08276253 x = -12.08276253 Simplifying x = -12.08276253Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.08276253, -12.08276253}
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