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Simplifying x2 + -30x + -25 = 40x + 100 Reorder the terms: -25 + -30x + x2 = 40x + 100 Reorder the terms: -25 + -30x + x2 = 100 + 40x Solving -25 + -30x + x2 = 100 + 40x Solving for variable 'x'. Reorder the terms: -25 + -100 + -30x + -40x + x2 = 100 + 40x + -100 + -40x Combine like terms: -25 + -100 = -125 -125 + -30x + -40x + x2 = 100 + 40x + -100 + -40x Combine like terms: -30x + -40x = -70x -125 + -70x + x2 = 100 + 40x + -100 + -40x Reorder the terms: -125 + -70x + x2 = 100 + -100 + 40x + -40x Combine like terms: 100 + -100 = 0 -125 + -70x + x2 = 0 + 40x + -40x -125 + -70x + x2 = 40x + -40x Combine like terms: 40x + -40x = 0 -125 + -70x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + -70x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + -70x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + -70x + x2 = 0 + 125 -70x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 -70x + x2 = 125 The x term is -70x. Take half its coefficient (-35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. -70x + 1225 + x2 = 125 + 1225 Reorder the terms: 1225 + -70x + x2 = 125 + 1225 Combine like terms: 125 + 1225 = 1350 1225 + -70x + x2 = 1350 Factor a perfect square on the left side: (x + -35)(x + -35) = 1350 Calculate the square root of the right side: 36.742346142 Break this problem into two subproblems by setting (x + -35) equal to 36.742346142 and -36.742346142.Subproblem 1
x + -35 = 36.742346142 Simplifying x + -35 = 36.742346142 Reorder the terms: -35 + x = 36.742346142 Solving -35 + x = 36.742346142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = 36.742346142 + 35 Combine like terms: -35 + 35 = 0 0 + x = 36.742346142 + 35 x = 36.742346142 + 35 Combine like terms: 36.742346142 + 35 = 71.742346142 x = 71.742346142 Simplifying x = 71.742346142Subproblem 2
x + -35 = -36.742346142 Simplifying x + -35 = -36.742346142 Reorder the terms: -35 + x = -36.742346142 Solving -35 + x = -36.742346142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = -36.742346142 + 35 Combine like terms: -35 + 35 = 0 0 + x = -36.742346142 + 35 x = -36.742346142 + 35 Combine like terms: -36.742346142 + 35 = -1.742346142 x = -1.742346142 Simplifying x = -1.742346142Solution
The solution to the problem is based on the solutions from the subproblems. x = {71.742346142, -1.742346142}
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