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Simplifying 70.4x + -0.8x2 = 965.6 Solving 70.4x + -0.8x2 = 965.6 Solving for variable 'x'. Reorder the terms: -965.6 + 70.4x + -0.8x2 = 965.6 + -965.6 Combine like terms: 965.6 + -965.6 = 0.0 -965.6 + 70.4x + -0.8x2 = 0.0 Begin completing the square. Divide all terms by -0.8 the coefficient of the squared term: Divide each side by '-0.8'. 1207 + -88x + x2 = 0 Move the constant term to the right: Add '-1207' to each side of the equation. 1207 + -88x + -1207 + x2 = 0 + -1207 Reorder the terms: 1207 + -1207 + -88x + x2 = 0 + -1207 Combine like terms: 1207 + -1207 = 0 0 + -88x + x2 = 0 + -1207 -88x + x2 = 0 + -1207 Combine like terms: 0 + -1207 = -1207 -88x + x2 = -1207 The x term is -88x. Take half its coefficient (-44). Square it (1936) and add it to both sides. Add '1936' to each side of the equation. -88x + 1936 + x2 = -1207 + 1936 Reorder the terms: 1936 + -88x + x2 = -1207 + 1936 Combine like terms: -1207 + 1936 = 729 1936 + -88x + x2 = 729 Factor a perfect square on the left side: (x + -44)(x + -44) = 729 Calculate the square root of the right side: 27 Break this problem into two subproblems by setting (x + -44) equal to 27 and -27.Subproblem 1
x + -44 = 27 Simplifying x + -44 = 27 Reorder the terms: -44 + x = 27 Solving -44 + x = 27 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44' to each side of the equation. -44 + 44 + x = 27 + 44 Combine like terms: -44 + 44 = 0 0 + x = 27 + 44 x = 27 + 44 Combine like terms: 27 + 44 = 71 x = 71 Simplifying x = 71Subproblem 2
x + -44 = -27 Simplifying x + -44 = -27 Reorder the terms: -44 + x = -27 Solving -44 + x = -27 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44' to each side of the equation. -44 + 44 + x = -27 + 44 Combine like terms: -44 + 44 = 0 0 + x = -27 + 44 x = -27 + 44 Combine like terms: -27 + 44 = 17 x = 17 Simplifying x = 17Solution
The solution to the problem is based on the solutions from the subproblems. x = {71, 17}
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