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Simplifying 0.05x2 + 10.2x + -107 = 0 Reorder the terms: -107 + 10.2x + 0.05x2 = 0 Solving -107 + 10.2x + 0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -2140 + 204x + x2 = 0 Move the constant term to the right: Add '2140' to each side of the equation. -2140 + 204x + 2140 + x2 = 0 + 2140 Reorder the terms: -2140 + 2140 + 204x + x2 = 0 + 2140 Combine like terms: -2140 + 2140 = 0 0 + 204x + x2 = 0 + 2140 204x + x2 = 0 + 2140 Combine like terms: 0 + 2140 = 2140 204x + x2 = 2140 The x term is 204x. Take half its coefficient (102). Square it (10404) and add it to both sides. Add '10404' to each side of the equation. 204x + 10404 + x2 = 2140 + 10404 Reorder the terms: 10404 + 204x + x2 = 2140 + 10404 Combine like terms: 2140 + 10404 = 12544 10404 + 204x + x2 = 12544 Factor a perfect square on the left side: (x + 102)(x + 102) = 12544 Calculate the square root of the right side: 112 Break this problem into two subproblems by setting (x + 102) equal to 112 and -112.Subproblem 1
x + 102 = 112 Simplifying x + 102 = 112 Reorder the terms: 102 + x = 112 Solving 102 + x = 112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-102' to each side of the equation. 102 + -102 + x = 112 + -102 Combine like terms: 102 + -102 = 0 0 + x = 112 + -102 x = 112 + -102 Combine like terms: 112 + -102 = 10 x = 10 Simplifying x = 10Subproblem 2
x + 102 = -112 Simplifying x + 102 = -112 Reorder the terms: 102 + x = -112 Solving 102 + x = -112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-102' to each side of the equation. 102 + -102 + x = -112 + -102 Combine like terms: 102 + -102 = 0 0 + x = -112 + -102 x = -112 + -102 Combine like terms: -112 + -102 = -214 x = -214 Simplifying x = -214Solution
The solution to the problem is based on the solutions from the subproblems. x = {10, -214}
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