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Simplifying 0.5x(x + 3) = 25 Reorder the terms: 0.5x(3 + x) = 25 (3 * 0.5x + x * 0.5x) = 25 (1.5x + 0.5x2) = 25 Solving 1.5x + 0.5x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + 1.5x + 0.5x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 1.5x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -50 + 3x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 3x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 3x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 3x + x2 = 0 + 50 3x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 3x + x2 = 50 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 50 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 50 + 2.25 Combine like terms: 50 + 2.25 = 52.25 2.25 + 3x + x2 = 52.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (x + 1.5) equal to 7.228416147 and -7.228416147.Subproblem 1
x + 1.5 = 7.228416147 Simplifying x + 1.5 = 7.228416147 Reorder the terms: 1.5 + x = 7.228416147 Solving 1.5 + x = 7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 7.228416147 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.228416147 + -1.5 x = 7.228416147 + -1.5 Combine like terms: 7.228416147 + -1.5 = 5.728416147 x = 5.728416147 Simplifying x = 5.728416147Subproblem 2
x + 1.5 = -7.228416147 Simplifying x + 1.5 = -7.228416147 Reorder the terms: 1.5 + x = -7.228416147 Solving 1.5 + x = -7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -7.228416147 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.228416147 + -1.5 x = -7.228416147 + -1.5 Combine like terms: -7.228416147 + -1.5 = -8.728416147 x = -8.728416147 Simplifying x = -8.728416147Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.728416147, -8.728416147}
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