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Simplifying -56x2 + 800x + 30000 = 0 Reorder the terms: 30000 + 800x + -56x2 = 0 Solving 30000 + 800x + -56x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(3750 + 100x + -7x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(3750 + 100x + -7x2)' equal to zero and attempt to solve: Simplifying 3750 + 100x + -7x2 = 0 Solving 3750 + 100x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -535.7142857 + -14.28571429x + x2 = 0 Move the constant term to the right: Add '535.7142857' to each side of the equation. -535.7142857 + -14.28571429x + 535.7142857 + x2 = 0 + 535.7142857 Reorder the terms: -535.7142857 + 535.7142857 + -14.28571429x + x2 = 0 + 535.7142857 Combine like terms: -535.7142857 + 535.7142857 = 0.0000000 0.0000000 + -14.28571429x + x2 = 0 + 535.7142857 -14.28571429x + x2 = 0 + 535.7142857 Combine like terms: 0 + 535.7142857 = 535.7142857 -14.28571429x + x2 = 535.7142857 The x term is -14.28571429x. Take half its coefficient (-7.142857145). Square it (51.02040819) and add it to both sides. Add '51.02040819' to each side of the equation. -14.28571429x + 51.02040819 + x2 = 535.7142857 + 51.02040819 Reorder the terms: 51.02040819 + -14.28571429x + x2 = 535.7142857 + 51.02040819 Combine like terms: 535.7142857 + 51.02040819 = 586.73469389 51.02040819 + -14.28571429x + x2 = 586.73469389 Factor a perfect square on the left side: (x + -7.142857145)(x + -7.142857145) = 586.73469389 Calculate the square root of the right side: 24.222607083 Break this problem into two subproblems by setting (x + -7.142857145) equal to 24.222607083 and -24.222607083.Subproblem 1
x + -7.142857145 = 24.222607083 Simplifying x + -7.142857145 = 24.222607083 Reorder the terms: -7.142857145 + x = 24.222607083 Solving -7.142857145 + x = 24.222607083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.142857145' to each side of the equation. -7.142857145 + 7.142857145 + x = 24.222607083 + 7.142857145 Combine like terms: -7.142857145 + 7.142857145 = 0.000000000 0.000000000 + x = 24.222607083 + 7.142857145 x = 24.222607083 + 7.142857145 Combine like terms: 24.222607083 + 7.142857145 = 31.365464228 x = 31.365464228 Simplifying x = 31.365464228Subproblem 2
x + -7.142857145 = -24.222607083 Simplifying x + -7.142857145 = -24.222607083 Reorder the terms: -7.142857145 + x = -24.222607083 Solving -7.142857145 + x = -24.222607083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.142857145' to each side of the equation. -7.142857145 + 7.142857145 + x = -24.222607083 + 7.142857145 Combine like terms: -7.142857145 + 7.142857145 = 0.000000000 0.000000000 + x = -24.222607083 + 7.142857145 x = -24.222607083 + 7.142857145 Combine like terms: -24.222607083 + 7.142857145 = -17.079749938 x = -17.079749938 Simplifying x = -17.079749938Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.365464228, -17.079749938}Solution
x = {31.365464228, -17.079749938}
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