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Simplifying 897.86 = 4x2 + -100x2 + 600x Reorder the terms: 897.86 = 600x + 4x2 + -100x2 Combine like terms: 4x2 + -100x2 = -96x2 897.86 = 600x + -96x2 Solving 897.86 = 600x + -96x2 Solving for variable 'x'. Reorder the terms: 897.86 + -600x + 96x2 = 600x + -600x + -96x2 + 96x2 Combine like terms: 600x + -600x = 0 897.86 + -600x + 96x2 = 0 + -96x2 + 96x2 897.86 + -600x + 96x2 = -96x2 + 96x2 Combine like terms: -96x2 + 96x2 = 0 897.86 + -600x + 96x2 = 0 Begin completing the square. Divide all terms by 96 the coefficient of the squared term: Divide each side by '96'. 9.352708333 + -6.25x + x2 = 0 Move the constant term to the right: Add '-9.352708333' to each side of the equation. 9.352708333 + -6.25x + -9.352708333 + x2 = 0 + -9.352708333 Reorder the terms: 9.352708333 + -9.352708333 + -6.25x + x2 = 0 + -9.352708333 Combine like terms: 9.352708333 + -9.352708333 = 0.000000000 0.000000000 + -6.25x + x2 = 0 + -9.352708333 -6.25x + x2 = 0 + -9.352708333 Combine like terms: 0 + -9.352708333 = -9.352708333 -6.25x + x2 = -9.352708333 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = -9.352708333 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = -9.352708333 + 9.765625 Combine like terms: -9.352708333 + 9.765625 = 0.412916667 9.765625 + -6.25x + x2 = 0.412916667 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 0.412916667 Calculate the square root of the right side: 0.642585922 Break this problem into two subproblems by setting (x + -3.125) equal to 0.642585922 and -0.642585922.Subproblem 1
x + -3.125 = 0.642585922 Simplifying x + -3.125 = 0.642585922 Reorder the terms: -3.125 + x = 0.642585922 Solving -3.125 + x = 0.642585922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 0.642585922 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 0.642585922 + 3.125 x = 0.642585922 + 3.125 Combine like terms: 0.642585922 + 3.125 = 3.767585922 x = 3.767585922 Simplifying x = 3.767585922Subproblem 2
x + -3.125 = -0.642585922 Simplifying x + -3.125 = -0.642585922 Reorder the terms: -3.125 + x = -0.642585922 Solving -3.125 + x = -0.642585922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -0.642585922 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -0.642585922 + 3.125 x = -0.642585922 + 3.125 Combine like terms: -0.642585922 + 3.125 = 2.482414078 x = 2.482414078 Simplifying x = 2.482414078Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.767585922, 2.482414078}
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