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Simplifying 16(9x2 + -100x + -5062500) = 0 Reorder the terms: 16(-5062500 + -100x + 9x2) = 0 (-5062500 * 16 + -100x * 16 + 9x2 * 16) = 0 (-81000000 + -1600x + 144x2) = 0 Solving -81000000 + -1600x + 144x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(-5062500 + -100x + 9x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-5062500 + -100x + 9x2)' equal to zero and attempt to solve: Simplifying -5062500 + -100x + 9x2 = 0 Solving -5062500 + -100x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -562500 + -11.11111111x + x2 = 0 Move the constant term to the right: Add '562500' to each side of the equation. -562500 + -11.11111111x + 562500 + x2 = 0 + 562500 Reorder the terms: -562500 + 562500 + -11.11111111x + x2 = 0 + 562500 Combine like terms: -562500 + 562500 = 0 0 + -11.11111111x + x2 = 0 + 562500 -11.11111111x + x2 = 0 + 562500 Combine like terms: 0 + 562500 = 562500 -11.11111111x + x2 = 562500 The x term is -11.11111111x. Take half its coefficient (-5.555555555). Square it (30.86419752) and add it to both sides. Add '30.86419752' to each side of the equation. -11.11111111x + 30.86419752 + x2 = 562500 + 30.86419752 Reorder the terms: 30.86419752 + -11.11111111x + x2 = 562500 + 30.86419752 Combine like terms: 562500 + 30.86419752 = 562530.86419752 30.86419752 + -11.11111111x + x2 = 562530.86419752 Factor a perfect square on the left side: (x + -5.555555555)(x + -5.555555555) = 562530.86419752 Calculate the square root of the right side: 750.020575849 Break this problem into two subproblems by setting (x + -5.555555555) equal to 750.020575849 and -750.020575849.Subproblem 1
x + -5.555555555 = 750.020575849 Simplifying x + -5.555555555 = 750.020575849 Reorder the terms: -5.555555555 + x = 750.020575849 Solving -5.555555555 + x = 750.020575849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.555555555' to each side of the equation. -5.555555555 + 5.555555555 + x = 750.020575849 + 5.555555555 Combine like terms: -5.555555555 + 5.555555555 = 0.000000000 0.000000000 + x = 750.020575849 + 5.555555555 x = 750.020575849 + 5.555555555 Combine like terms: 750.020575849 + 5.555555555 = 755.576131404 x = 755.576131404 Simplifying x = 755.576131404Subproblem 2
x + -5.555555555 = -750.020575849 Simplifying x + -5.555555555 = -750.020575849 Reorder the terms: -5.555555555 + x = -750.020575849 Solving -5.555555555 + x = -750.020575849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.555555555' to each side of the equation. -5.555555555 + 5.555555555 + x = -750.020575849 + 5.555555555 Combine like terms: -5.555555555 + 5.555555555 = 0.000000000 0.000000000 + x = -750.020575849 + 5.555555555 x = -750.020575849 + 5.555555555 Combine like terms: -750.020575849 + 5.555555555 = -744.465020294 x = -744.465020294 Simplifying x = -744.465020294Solution
The solution to the problem is based on the solutions from the subproblems. x = {755.576131404, -744.465020294}Solution
x = {755.576131404, -744.465020294}
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