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Simplifying 25x2 + -40x + -32 = 22 Reorder the terms: -32 + -40x + 25x2 = 22 Solving -32 + -40x + 25x2 = 22 Solving for variable 'x'. Reorder the terms: -32 + -22 + -40x + 25x2 = 22 + -22 Combine like terms: -32 + -22 = -54 -54 + -40x + 25x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -54 + -40x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -2.16 + -1.6x + x2 = 0 Move the constant term to the right: Add '2.16' to each side of the equation. -2.16 + -1.6x + 2.16 + x2 = 0 + 2.16 Reorder the terms: -2.16 + 2.16 + -1.6x + x2 = 0 + 2.16 Combine like terms: -2.16 + 2.16 = 0.00 0.00 + -1.6x + x2 = 0 + 2.16 -1.6x + x2 = 0 + 2.16 Combine like terms: 0 + 2.16 = 2.16 -1.6x + x2 = 2.16 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 2.16 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 2.16 + 0.64 Combine like terms: 2.16 + 0.64 = 2.8 0.64 + -1.6x + x2 = 2.8 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 2.8 Calculate the square root of the right side: 1.673320053 Break this problem into two subproblems by setting (x + -0.8) equal to 1.673320053 and -1.673320053.Subproblem 1
x + -0.8 = 1.673320053 Simplifying x + -0.8 = 1.673320053 Reorder the terms: -0.8 + x = 1.673320053 Solving -0.8 + x = 1.673320053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 1.673320053 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 1.673320053 + 0.8 x = 1.673320053 + 0.8 Combine like terms: 1.673320053 + 0.8 = 2.473320053 x = 2.473320053 Simplifying x = 2.473320053Subproblem 2
x + -0.8 = -1.673320053 Simplifying x + -0.8 = -1.673320053 Reorder the terms: -0.8 + x = -1.673320053 Solving -0.8 + x = -1.673320053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -1.673320053 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -1.673320053 + 0.8 x = -1.673320053 + 0.8 Combine like terms: -1.673320053 + 0.8 = -0.873320053 x = -0.873320053 Simplifying x = -0.873320053Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.473320053, -0.873320053}
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