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Simplifying 3x(0.5x + 5) = 26 Reorder the terms: 3x(5 + 0.5x) = 26 (5 * 3x + 0.5x * 3x) = 26 (15x + 1.5x2) = 26 Solving 15x + 1.5x2 = 26 Solving for variable 'x'. Reorder the terms: -26 + 15x + 1.5x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + 15x + 1.5x2 = 0 Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. -17.33333333 + 10x + x2 = 0 Move the constant term to the right: Add '17.33333333' to each side of the equation. -17.33333333 + 10x + 17.33333333 + x2 = 0 + 17.33333333 Reorder the terms: -17.33333333 + 17.33333333 + 10x + x2 = 0 + 17.33333333 Combine like terms: -17.33333333 + 17.33333333 = 0.00000000 0.00000000 + 10x + x2 = 0 + 17.33333333 10x + x2 = 0 + 17.33333333 Combine like terms: 0 + 17.33333333 = 17.33333333 10x + x2 = 17.33333333 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 17.33333333 + 25 Reorder the terms: 25 + 10x + x2 = 17.33333333 + 25 Combine like terms: 17.33333333 + 25 = 42.33333333 25 + 10x + x2 = 42.33333333 Factor a perfect square on the left side: (x + 5)(x + 5) = 42.33333333 Calculate the square root of the right side: 6.506407098 Break this problem into two subproblems by setting (x + 5) equal to 6.506407098 and -6.506407098.Subproblem 1
x + 5 = 6.506407098 Simplifying x + 5 = 6.506407098 Reorder the terms: 5 + x = 6.506407098 Solving 5 + x = 6.506407098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 6.506407098 + -5 Combine like terms: 5 + -5 = 0 0 + x = 6.506407098 + -5 x = 6.506407098 + -5 Combine like terms: 6.506407098 + -5 = 1.506407098 x = 1.506407098 Simplifying x = 1.506407098Subproblem 2
x + 5 = -6.506407098 Simplifying x + 5 = -6.506407098 Reorder the terms: 5 + x = -6.506407098 Solving 5 + x = -6.506407098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -6.506407098 + -5 Combine like terms: 5 + -5 = 0 0 + x = -6.506407098 + -5 x = -6.506407098 + -5 Combine like terms: -6.506407098 + -5 = -11.506407098 x = -11.506407098 Simplifying x = -11.506407098Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.506407098, -11.506407098}
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