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Simplifying 25x2 + -60x + -36 = 0 Reorder the terms: -36 + -60x + 25x2 = 0 Solving -36 + -60x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.44 + -2.4x + x2 = 0 Move the constant term to the right: Add '1.44' to each side of the equation. -1.44 + -2.4x + 1.44 + x2 = 0 + 1.44 Reorder the terms: -1.44 + 1.44 + -2.4x + x2 = 0 + 1.44 Combine like terms: -1.44 + 1.44 = 0.00 0.00 + -2.4x + x2 = 0 + 1.44 -2.4x + x2 = 0 + 1.44 Combine like terms: 0 + 1.44 = 1.44 -2.4x + x2 = 1.44 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 1.44 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 1.44 + 1.44 Combine like terms: 1.44 + 1.44 = 2.88 1.44 + -2.4x + x2 = 2.88 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 2.88 Calculate the square root of the right side: 1.697056275 Break this problem into two subproblems by setting (x + -1.2) equal to 1.697056275 and -1.697056275.Subproblem 1
x + -1.2 = 1.697056275 Simplifying x + -1.2 = 1.697056275 Reorder the terms: -1.2 + x = 1.697056275 Solving -1.2 + x = 1.697056275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 1.697056275 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 1.697056275 + 1.2 x = 1.697056275 + 1.2 Combine like terms: 1.697056275 + 1.2 = 2.897056275 x = 2.897056275 Simplifying x = 2.897056275Subproblem 2
x + -1.2 = -1.697056275 Simplifying x + -1.2 = -1.697056275 Reorder the terms: -1.2 + x = -1.697056275 Solving -1.2 + x = -1.697056275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -1.697056275 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -1.697056275 + 1.2 x = -1.697056275 + 1.2 Combine like terms: -1.697056275 + 1.2 = -0.497056275 x = -0.497056275 Simplifying x = -0.497056275Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.897056275, -0.497056275}
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