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Simplifying 10x2 + -99x + 200 = 0 Reorder the terms: 200 + -99x + 10x2 = 0 Solving 200 + -99x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 20 + -9.9x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -9.9x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -9.9x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -9.9x + x2 = 0 + -20 -9.9x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -9.9x + x2 = -20 The x term is -9.9x. Take half its coefficient (-4.95). Square it (24.5025) and add it to both sides. Add '24.5025' to each side of the equation. -9.9x + 24.5025 + x2 = -20 + 24.5025 Reorder the terms: 24.5025 + -9.9x + x2 = -20 + 24.5025 Combine like terms: -20 + 24.5025 = 4.5025 24.5025 + -9.9x + x2 = 4.5025 Factor a perfect square on the left side: (x + -4.95)(x + -4.95) = 4.5025 Calculate the square root of the right side: 2.121909517 Break this problem into two subproblems by setting (x + -4.95) equal to 2.121909517 and -2.121909517.Subproblem 1
x + -4.95 = 2.121909517 Simplifying x + -4.95 = 2.121909517 Reorder the terms: -4.95 + x = 2.121909517 Solving -4.95 + x = 2.121909517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.95' to each side of the equation. -4.95 + 4.95 + x = 2.121909517 + 4.95 Combine like terms: -4.95 + 4.95 = 0.00 0.00 + x = 2.121909517 + 4.95 x = 2.121909517 + 4.95 Combine like terms: 2.121909517 + 4.95 = 7.071909517 x = 7.071909517 Simplifying x = 7.071909517Subproblem 2
x + -4.95 = -2.121909517 Simplifying x + -4.95 = -2.121909517 Reorder the terms: -4.95 + x = -2.121909517 Solving -4.95 + x = -2.121909517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.95' to each side of the equation. -4.95 + 4.95 + x = -2.121909517 + 4.95 Combine like terms: -4.95 + 4.95 = 0.00 0.00 + x = -2.121909517 + 4.95 x = -2.121909517 + 4.95 Combine like terms: -2.121909517 + 4.95 = 2.828090483 x = 2.828090483 Simplifying x = 2.828090483Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.071909517, 2.828090483}
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