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Simplifying -25x2 + -60x = -31 Reorder the terms: -60x + -25x2 = -31 Solving -60x + -25x2 = -31 Solving for variable 'x'. Reorder the terms: 31 + -60x + -25x2 = -31 + 31 Combine like terms: -31 + 31 = 0 31 + -60x + -25x2 = 0 Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -1.24 + 2.4x + x2 = 0 Move the constant term to the right: Add '1.24' to each side of the equation. -1.24 + 2.4x + 1.24 + x2 = 0 + 1.24 Reorder the terms: -1.24 + 1.24 + 2.4x + x2 = 0 + 1.24 Combine like terms: -1.24 + 1.24 = 0.00 0.00 + 2.4x + x2 = 0 + 1.24 2.4x + x2 = 0 + 1.24 Combine like terms: 0 + 1.24 = 1.24 2.4x + x2 = 1.24 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 = 1.24 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 1.24 + 1.44 Combine like terms: 1.24 + 1.44 = 2.68 1.44 + 2.4x + x2 = 2.68 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 2.68 Calculate the square root of the right side: 1.637070554 Break this problem into two subproblems by setting (x + 1.2) equal to 1.637070554 and -1.637070554.Subproblem 1
x + 1.2 = 1.637070554 Simplifying x + 1.2 = 1.637070554 Reorder the terms: 1.2 + x = 1.637070554 Solving 1.2 + x = 1.637070554 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 = 1.637070554 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 1.637070554 + -1.2 x = 1.637070554 + -1.2 Combine like terms: 1.637070554 + -1.2 = 0.437070554 x = 0.437070554 Simplifying x = 0.437070554Subproblem 2
x + 1.2 = -1.637070554 Simplifying x + 1.2 = -1.637070554 Reorder the terms: 1.2 + x = -1.637070554 Solving 1.2 + x = -1.637070554 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 = -1.637070554 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -1.637070554 + -1.2 x = -1.637070554 + -1.2 Combine like terms: -1.637070554 + -1.2 = -2.837070554 x = -2.837070554 Simplifying x = -2.837070554Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.437070554, -2.837070554}
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