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Simplifying 1.25x2 + -40x = 64 Reorder the terms: -40x + 1.25x2 = 64 Solving -40x + 1.25x2 = 64 Solving for variable 'x'. Reorder the terms: -64 + -40x + 1.25x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + -40x + 1.25x2 = 0 Begin completing the square. Divide all terms by 1.25 the coefficient of the squared term: Divide each side by '1.25'. -51.2 + -32x + x2 = 0 Move the constant term to the right: Add '51.2' to each side of the equation. -51.2 + -32x + 51.2 + x2 = 0 + 51.2 Reorder the terms: -51.2 + 51.2 + -32x + x2 = 0 + 51.2 Combine like terms: -51.2 + 51.2 = 0.0 0.0 + -32x + x2 = 0 + 51.2 -32x + x2 = 0 + 51.2 Combine like terms: 0 + 51.2 = 51.2 -32x + x2 = 51.2 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = 51.2 + 256 Reorder the terms: 256 + -32x + x2 = 51.2 + 256 Combine like terms: 51.2 + 256 = 307.2 256 + -32x + x2 = 307.2 Factor a perfect square on the left side: (x + -16)(x + -16) = 307.2 Calculate the square root of the right side: 17.52712184 Break this problem into two subproblems by setting (x + -16) equal to 17.52712184 and -17.52712184.Subproblem 1
x + -16 = 17.52712184 Simplifying x + -16 = 17.52712184 Reorder the terms: -16 + x = 17.52712184 Solving -16 + x = 17.52712184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 17.52712184 + 16 Combine like terms: -16 + 16 = 0 0 + x = 17.52712184 + 16 x = 17.52712184 + 16 Combine like terms: 17.52712184 + 16 = 33.52712184 x = 33.52712184 Simplifying x = 33.52712184Subproblem 2
x + -16 = -17.52712184 Simplifying x + -16 = -17.52712184 Reorder the terms: -16 + x = -17.52712184 Solving -16 + x = -17.52712184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -17.52712184 + 16 Combine like terms: -16 + 16 = 0 0 + x = -17.52712184 + 16 x = -17.52712184 + 16 Combine like terms: -17.52712184 + 16 = -1.52712184 x = -1.52712184 Simplifying x = -1.52712184Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.52712184, -1.52712184}
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