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Simplifying 5.07x2 + -10.99x + 3.31 = 0 Reorder the terms: 3.31 + -10.99x + 5.07x2 = 0 Solving 3.31 + -10.99x + 5.07x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5.07 the coefficient of the squared term: Divide each side by '5.07'. 0.6528599606 + -2.16765286x + x2 = 0 Move the constant term to the right: Add '-0.6528599606' to each side of the equation. 0.6528599606 + -2.16765286x + -0.6528599606 + x2 = 0 + -0.6528599606 Reorder the terms: 0.6528599606 + -0.6528599606 + -2.16765286x + x2 = 0 + -0.6528599606 Combine like terms: 0.6528599606 + -0.6528599606 = 0.0000000000 0.0000000000 + -2.16765286x + x2 = 0 + -0.6528599606 -2.16765286x + x2 = 0 + -0.6528599606 Combine like terms: 0 + -0.6528599606 = -0.6528599606 -2.16765286x + x2 = -0.6528599606 The x term is -2.16765286x. Take half its coefficient (-1.08382643). Square it (1.174679730) and add it to both sides. Add '1.174679730' to each side of the equation. -2.16765286x + 1.174679730 + x2 = -0.6528599606 + 1.174679730 Reorder the terms: 1.174679730 + -2.16765286x + x2 = -0.6528599606 + 1.174679730 Combine like terms: -0.6528599606 + 1.174679730 = 0.5218197694 1.174679730 + -2.16765286x + x2 = 0.5218197694 Factor a perfect square on the left side: (x + -1.08382643)(x + -1.08382643) = 0.5218197694 Calculate the square root of the right side: 0.722370936 Break this problem into two subproblems by setting (x + -1.08382643) equal to 0.722370936 and -0.722370936.Subproblem 1
x + -1.08382643 = 0.722370936 Simplifying x + -1.08382643 = 0.722370936 Reorder the terms: -1.08382643 + x = 0.722370936 Solving -1.08382643 + x = 0.722370936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.08382643' to each side of the equation. -1.08382643 + 1.08382643 + x = 0.722370936 + 1.08382643 Combine like terms: -1.08382643 + 1.08382643 = 0.00000000 0.00000000 + x = 0.722370936 + 1.08382643 x = 0.722370936 + 1.08382643 Combine like terms: 0.722370936 + 1.08382643 = 1.806197366 x = 1.806197366 Simplifying x = 1.806197366Subproblem 2
x + -1.08382643 = -0.722370936 Simplifying x + -1.08382643 = -0.722370936 Reorder the terms: -1.08382643 + x = -0.722370936 Solving -1.08382643 + x = -0.722370936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.08382643' to each side of the equation. -1.08382643 + 1.08382643 + x = -0.722370936 + 1.08382643 Combine like terms: -1.08382643 + 1.08382643 = 0.00000000 0.00000000 + x = -0.722370936 + 1.08382643 x = -0.722370936 + 1.08382643 Combine like terms: -0.722370936 + 1.08382643 = 0.361455494 x = 0.361455494 Simplifying x = 0.361455494Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.806197366, 0.361455494}
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