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Simplifying 74.016 = 1117.72x + 21.338x2 Solving 74.016 = 1117.72x + 21.338x2 Solving for variable 'x'. Reorder the terms: 74.016 + -1117.72x + -21.338x2 = 1117.72x + -1117.72x + 21.338x2 + -21.338x2 Combine like terms: 1117.72x + -1117.72x = 0.00 74.016 + -1117.72x + -21.338x2 = 0.00 + 21.338x2 + -21.338x2 74.016 + -1117.72x + -21.338x2 = 21.338x2 + -21.338x2 Combine like terms: 21.338x2 + -21.338x2 = 0.000 74.016 + -1117.72x + -21.338x2 = 0.000 Begin completing the square. Divide all terms by -21.338 the coefficient of the squared term: Divide each side by '-21.338'. -3.468741213 + 52.38166651x + x2 = 0 Move the constant term to the right: Add '3.468741213' to each side of the equation. -3.468741213 + 52.38166651x + 3.468741213 + x2 = 0 + 3.468741213 Reorder the terms: -3.468741213 + 3.468741213 + 52.38166651x + x2 = 0 + 3.468741213 Combine like terms: -3.468741213 + 3.468741213 = 0.000000000 0.000000000 + 52.38166651x + x2 = 0 + 3.468741213 52.38166651x + x2 = 0 + 3.468741213 Combine like terms: 0 + 3.468741213 = 3.468741213 52.38166651x + x2 = 3.468741213 The x term is 52.38166651x. Take half its coefficient (26.19083326). Square it (685.9597469) and add it to both sides. Add '685.9597469' to each side of the equation. 52.38166651x + 685.9597469 + x2 = 3.468741213 + 685.9597469 Reorder the terms: 685.9597469 + 52.38166651x + x2 = 3.468741213 + 685.9597469 Combine like terms: 3.468741213 + 685.9597469 = 689.428488113 685.9597469 + 52.38166651x + x2 = 689.428488113 Factor a perfect square on the left side: (x + 26.19083326)(x + 26.19083326) = 689.428488113 Calculate the square root of the right side: 26.256970277 Break this problem into two subproblems by setting (x + 26.19083326) equal to 26.256970277 and -26.256970277.Subproblem 1
x + 26.19083326 = 26.256970277 Simplifying x + 26.19083326 = 26.256970277 Reorder the terms: 26.19083326 + x = 26.256970277 Solving 26.19083326 + x = 26.256970277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26.19083326' to each side of the equation. 26.19083326 + -26.19083326 + x = 26.256970277 + -26.19083326 Combine like terms: 26.19083326 + -26.19083326 = 0.00000000 0.00000000 + x = 26.256970277 + -26.19083326 x = 26.256970277 + -26.19083326 Combine like terms: 26.256970277 + -26.19083326 = 0.066137017 x = 0.066137017 Simplifying x = 0.066137017Subproblem 2
x + 26.19083326 = -26.256970277 Simplifying x + 26.19083326 = -26.256970277 Reorder the terms: 26.19083326 + x = -26.256970277 Solving 26.19083326 + x = -26.256970277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26.19083326' to each side of the equation. 26.19083326 + -26.19083326 + x = -26.256970277 + -26.19083326 Combine like terms: 26.19083326 + -26.19083326 = 0.00000000 0.00000000 + x = -26.256970277 + -26.19083326 x = -26.256970277 + -26.19083326 Combine like terms: -26.256970277 + -26.19083326 = -52.447803537 x = -52.447803537 Simplifying x = -52.447803537Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.066137017, -52.447803537}
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