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Simplifying 6 = 0.10x(30 + x) 6 = (30 * 0.10x + x * 0.10x) 6 = (3x + 0.10x2) Solving 6 = 3x + 0.10x2 Solving for variable 'x'. Reorder the terms: 6 + -3x + -0.10x2 = 3x + -3x + 0.10x2 + -0.10x2 Combine like terms: 3x + -3x = 0 6 + -3x + -0.10x2 = 0 + 0.10x2 + -0.10x2 6 + -3x + -0.10x2 = 0.10x2 + -0.10x2 Combine like terms: 0.10x2 + -0.10x2 = 0.00 6 + -3x + -0.10x2 = 0.00 Begin completing the square. Divide all terms by -0.10 the coefficient of the squared term: Divide each side by '-0.10'. -60 + 30x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 30x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 30x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 30x + x2 = 0 + 60 30x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 30x + x2 = 60 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 60 + 225 Reorder the terms: 225 + 30x + x2 = 60 + 225 Combine like terms: 60 + 225 = 285 225 + 30x + x2 = 285 Factor a perfect square on the left side: (x + 15)(x + 15) = 285 Calculate the square root of the right side: 16.881943016 Break this problem into two subproblems by setting (x + 15) equal to 16.881943016 and -16.881943016.Subproblem 1
x + 15 = 16.881943016 Simplifying x + 15 = 16.881943016 Reorder the terms: 15 + x = 16.881943016 Solving 15 + x = 16.881943016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 16.881943016 + -15 Combine like terms: 15 + -15 = 0 0 + x = 16.881943016 + -15 x = 16.881943016 + -15 Combine like terms: 16.881943016 + -15 = 1.881943016 x = 1.881943016 Simplifying x = 1.881943016Subproblem 2
x + 15 = -16.881943016 Simplifying x + 15 = -16.881943016 Reorder the terms: 15 + x = -16.881943016 Solving 15 + x = -16.881943016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -16.881943016 + -15 Combine like terms: 15 + -15 = 0 0 + x = -16.881943016 + -15 x = -16.881943016 + -15 Combine like terms: -16.881943016 + -15 = -31.881943016 x = -31.881943016 Simplifying x = -31.881943016Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.881943016, -31.881943016}
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