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Simplifying x2 + 20x + -4900 = 0 Reorder the terms: -4900 + 20x + x2 = 0 Solving -4900 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4900' to each side of the equation. -4900 + 20x + 4900 + x2 = 0 + 4900 Reorder the terms: -4900 + 4900 + 20x + x2 = 0 + 4900 Combine like terms: -4900 + 4900 = 0 0 + 20x + x2 = 0 + 4900 20x + x2 = 0 + 4900 Combine like terms: 0 + 4900 = 4900 20x + x2 = 4900 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 4900 + 100 Reorder the terms: 100 + 20x + x2 = 4900 + 100 Combine like terms: 4900 + 100 = 5000 100 + 20x + x2 = 5000 Factor a perfect square on the left side: (x + 10)(x + 10) = 5000 Calculate the square root of the right side: 70.710678119 Break this problem into two subproblems by setting (x + 10) equal to 70.710678119 and -70.710678119.Subproblem 1
x + 10 = 70.710678119 Simplifying x + 10 = 70.710678119 Reorder the terms: 10 + x = 70.710678119 Solving 10 + x = 70.710678119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 70.710678119 + -10 Combine like terms: 10 + -10 = 0 0 + x = 70.710678119 + -10 x = 70.710678119 + -10 Combine like terms: 70.710678119 + -10 = 60.710678119 x = 60.710678119 Simplifying x = 60.710678119Subproblem 2
x + 10 = -70.710678119 Simplifying x + 10 = -70.710678119 Reorder the terms: 10 + x = -70.710678119 Solving 10 + x = -70.710678119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -70.710678119 + -10 Combine like terms: 10 + -10 = 0 0 + x = -70.710678119 + -10 x = -70.710678119 + -10 Combine like terms: -70.710678119 + -10 = -80.710678119 x = -80.710678119 Simplifying x = -80.710678119Solution
The solution to the problem is based on the solutions from the subproblems. x = {60.710678119, -80.710678119}
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