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Simplifying (x2) + -1(196x) + 3600 = 0 x2 + -1(196x) + 3600 = 0 Remove parenthesis around (196x) x2 + -1 * 196x + 3600 = 0 Multiply -1 * 196 x2 + -196x + 3600 = 0 Reorder the terms: 3600 + -196x + x2 = 0 Solving 3600 + -196x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3600' to each side of the equation. 3600 + -196x + -3600 + x2 = 0 + -3600 Reorder the terms: 3600 + -3600 + -196x + x2 = 0 + -3600 Combine like terms: 3600 + -3600 = 0 0 + -196x + x2 = 0 + -3600 -196x + x2 = 0 + -3600 Combine like terms: 0 + -3600 = -3600 -196x + x2 = -3600 The x term is -196x. Take half its coefficient (-98). Square it (9604) and add it to both sides. Add '9604' to each side of the equation. -196x + 9604 + x2 = -3600 + 9604 Reorder the terms: 9604 + -196x + x2 = -3600 + 9604 Combine like terms: -3600 + 9604 = 6004 9604 + -196x + x2 = 6004 Factor a perfect square on the left side: (x + -98)(x + -98) = 6004 Calculate the square root of the right side: 77.485482511 Break this problem into two subproblems by setting (x + -98) equal to 77.485482511 and -77.485482511.Subproblem 1
x + -98 = 77.485482511 Simplifying x + -98 = 77.485482511 Reorder the terms: -98 + x = 77.485482511 Solving -98 + x = 77.485482511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '98' to each side of the equation. -98 + 98 + x = 77.485482511 + 98 Combine like terms: -98 + 98 = 0 0 + x = 77.485482511 + 98 x = 77.485482511 + 98 Combine like terms: 77.485482511 + 98 = 175.485482511 x = 175.485482511 Simplifying x = 175.485482511Subproblem 2
x + -98 = -77.485482511 Simplifying x + -98 = -77.485482511 Reorder the terms: -98 + x = -77.485482511 Solving -98 + x = -77.485482511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '98' to each side of the equation. -98 + 98 + x = -77.485482511 + 98 Combine like terms: -98 + 98 = 0 0 + x = -77.485482511 + 98 x = -77.485482511 + 98 Combine like terms: -77.485482511 + 98 = 20.514517489 x = 20.514517489 Simplifying x = 20.514517489Solution
The solution to the problem is based on the solutions from the subproblems. x = {175.485482511, 20.514517489}
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