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Simplifying 2500x2 + 100x + 1100 = 20000 Reorder the terms: 1100 + 100x + 2500x2 = 20000 Solving 1100 + 100x + 2500x2 = 20000 Solving for variable 'x'. Reorder the terms: 1100 + -20000 + 100x + 2500x2 = 20000 + -20000 Combine like terms: 1100 + -20000 = -18900 -18900 + 100x + 2500x2 = 20000 + -20000 Combine like terms: 20000 + -20000 = 0 -18900 + 100x + 2500x2 = 0 Factor out the Greatest Common Factor (GCF), '100'. 100(-189 + x + 25x2) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(-189 + x + 25x2)' equal to zero and attempt to solve: Simplifying -189 + x + 25x2 = 0 Solving -189 + x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -7.56 + 0.04x + x2 = 0 Move the constant term to the right: Add '7.56' to each side of the equation. -7.56 + 0.04x + 7.56 + x2 = 0 + 7.56 Reorder the terms: -7.56 + 7.56 + 0.04x + x2 = 0 + 7.56 Combine like terms: -7.56 + 7.56 = 0.00 0.00 + 0.04x + x2 = 0 + 7.56 0.04x + x2 = 0 + 7.56 Combine like terms: 0 + 7.56 = 7.56 0.04x + x2 = 7.56 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.04x + 0.25 + x2 = 7.56 + 0.25 Reorder the terms: 0.25 + 0.04x + x2 = 7.56 + 0.25 Combine like terms: 7.56 + 0.25 = 7.81 0.25 + 0.04x + x2 = 7.81 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 7.81 Calculate the square root of the right side: 2.794637722 Break this problem into two subproblems by setting (x + 0.5) equal to 2.794637722 and -2.794637722.Subproblem 1
x + 0.5 = 2.794637722 Simplifying x + 0.5 = 2.794637722 Reorder the terms: 0.5 + x = 2.794637722 Solving 0.5 + x = 2.794637722 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.794637722 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.794637722 + -0.5 x = 2.794637722 + -0.5 Combine like terms: 2.794637722 + -0.5 = 2.294637722 x = 2.294637722 Simplifying x = 2.294637722Subproblem 2
x + 0.5 = -2.794637722 Simplifying x + 0.5 = -2.794637722 Reorder the terms: 0.5 + x = -2.794637722 Solving 0.5 + x = -2.794637722 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.794637722 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.794637722 + -0.5 x = -2.794637722 + -0.5 Combine like terms: -2.794637722 + -0.5 = -3.294637722 x = -3.294637722 Simplifying x = -3.294637722Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.294637722, -3.294637722}Solution
x = {2.294637722, -3.294637722}
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