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Simplifying 2x2 + 21x = 100 Reorder the terms: 21x + 2x2 = 100 Solving 21x + 2x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 21x + 2x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 21x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -50 + 10.5x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 10.5x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 10.5x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 10.5x + x2 = 0 + 50 10.5x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 10.5x + x2 = 50 The x term is 10.5x. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5x + 27.5625 + x2 = 50 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 50 + 27.5625 Combine like terms: 50 + 27.5625 = 77.5625 27.5625 + 10.5x + x2 = 77.5625 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 77.5625 Calculate the square root of the right side: 8.806957477 Break this problem into two subproblems by setting (x + 5.25) equal to 8.806957477 and -8.806957477.Subproblem 1
x + 5.25 = 8.806957477 Simplifying x + 5.25 = 8.806957477 Reorder the terms: 5.25 + x = 8.806957477 Solving 5.25 + x = 8.806957477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 8.806957477 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 8.806957477 + -5.25 x = 8.806957477 + -5.25 Combine like terms: 8.806957477 + -5.25 = 3.556957477 x = 3.556957477 Simplifying x = 3.556957477Subproblem 2
x + 5.25 = -8.806957477 Simplifying x + 5.25 = -8.806957477 Reorder the terms: 5.25 + x = -8.806957477 Solving 5.25 + x = -8.806957477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -8.806957477 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -8.806957477 + -5.25 x = -8.806957477 + -5.25 Combine like terms: -8.806957477 + -5.25 = -14.056957477 x = -14.056957477 Simplifying x = -14.056957477Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.556957477, -14.056957477}
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