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Simplifying 0.25x(x + -6) * 0.05 = 6.30 Reorder the terms: 0.25x(-6 + x) * 0.05 = 6.30 Reorder the terms for easier multiplication: 0.25 * 0.05x(-6 + x) = 6.30 Multiply 0.25 * 0.05 0.0125x(-6 + x) = 6.30 (-6 * 0.0125x + x * 0.0125x) = 6.30 (-0.075x + 0.0125x2) = 6.30 Solving -0.075x + 0.0125x2 = 6.30 Solving for variable 'x'. Reorder the terms: -6.30 + -0.075x + 0.0125x2 = 6.30 + -6.30 Combine like terms: 6.30 + -6.30 = 0.00 -6.30 + -0.075x + 0.0125x2 = 0.00 Begin completing the square. Divide all terms by 0.0125 the coefficient of the squared term: Divide each side by '0.0125'. -504 + -6x + x2 = 0 Move the constant term to the right: Add '504' to each side of the equation. -504 + -6x + 504 + x2 = 0 + 504 Reorder the terms: -504 + 504 + -6x + x2 = 0 + 504 Combine like terms: -504 + 504 = 0 0 + -6x + x2 = 0 + 504 -6x + x2 = 0 + 504 Combine like terms: 0 + 504 = 504 -6x + x2 = 504 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 504 + 9 Reorder the terms: 9 + -6x + x2 = 504 + 9 Combine like terms: 504 + 9 = 513 9 + -6x + x2 = 513 Factor a perfect square on the left side: (x + -3)(x + -3) = 513 Calculate the square root of the right side: 22.649503306 Break this problem into two subproblems by setting (x + -3) equal to 22.649503306 and -22.649503306.Subproblem 1
x + -3 = 22.649503306 Simplifying x + -3 = 22.649503306 Reorder the terms: -3 + x = 22.649503306 Solving -3 + x = 22.649503306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 22.649503306 + 3 Combine like terms: -3 + 3 = 0 0 + x = 22.649503306 + 3 x = 22.649503306 + 3 Combine like terms: 22.649503306 + 3 = 25.649503306 x = 25.649503306 Simplifying x = 25.649503306Subproblem 2
x + -3 = -22.649503306 Simplifying x + -3 = -22.649503306 Reorder the terms: -3 + x = -22.649503306 Solving -3 + x = -22.649503306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -22.649503306 + 3 Combine like terms: -3 + 3 = 0 0 + x = -22.649503306 + 3 x = -22.649503306 + 3 Combine like terms: -22.649503306 + 3 = -19.649503306 x = -19.649503306 Simplifying x = -19.649503306Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.649503306, -19.649503306}
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