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Simplifying 2x2 + 21x + -5.7 = 0 Reorder the terms: -5.7 + 21x + 2x2 = 0 Solving -5.7 + 21x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.85 + 10.5x + x2 = 0 Move the constant term to the right: Add '2.85' to each side of the equation. -2.85 + 10.5x + 2.85 + x2 = 0 + 2.85 Reorder the terms: -2.85 + 2.85 + 10.5x + x2 = 0 + 2.85 Combine like terms: -2.85 + 2.85 = 0.00 0.00 + 10.5x + x2 = 0 + 2.85 10.5x + x2 = 0 + 2.85 Combine like terms: 0 + 2.85 = 2.85 10.5x + x2 = 2.85 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 = 2.85 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 2.85 + 27.5625 Combine like terms: 2.85 + 27.5625 = 30.4125 27.5625 + 10.5x + x2 = 30.4125 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 30.4125 Calculate the square root of the right side: 5.514752941 Break this problem into two subproblems by setting (x + 5.25) equal to 5.514752941 and -5.514752941.Subproblem 1
x + 5.25 = 5.514752941 Simplifying x + 5.25 = 5.514752941 Reorder the terms: 5.25 + x = 5.514752941 Solving 5.25 + x = 5.514752941 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 = 5.514752941 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 5.514752941 + -5.25 x = 5.514752941 + -5.25 Combine like terms: 5.514752941 + -5.25 = 0.264752941 x = 0.264752941 Simplifying x = 0.264752941Subproblem 2
x + 5.25 = -5.514752941 Simplifying x + 5.25 = -5.514752941 Reorder the terms: 5.25 + x = -5.514752941 Solving 5.25 + x = -5.514752941 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 = -5.514752941 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -5.514752941 + -5.25 x = -5.514752941 + -5.25 Combine like terms: -5.514752941 + -5.25 = -10.764752941 x = -10.764752941 Simplifying x = -10.764752941Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.264752941, -10.764752941}
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