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Simplifying 3.76x2 + -9.65x + 2.61 = 0 Reorder the terms: 2.61 + -9.65x + 3.76x2 = 0 Solving 2.61 + -9.65x + 3.76x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.76 the coefficient of the squared term: Divide each side by '3.76'. 0.6941489362 + -2.566489362x + x2 = 0 Move the constant term to the right: Add '-0.6941489362' to each side of the equation. 0.6941489362 + -2.566489362x + -0.6941489362 + x2 = 0 + -0.6941489362 Reorder the terms: 0.6941489362 + -0.6941489362 + -2.566489362x + x2 = 0 + -0.6941489362 Combine like terms: 0.6941489362 + -0.6941489362 = 0.0000000000 0.0000000000 + -2.566489362x + x2 = 0 + -0.6941489362 -2.566489362x + x2 = 0 + -0.6941489362 Combine like terms: 0 + -0.6941489362 = -0.6941489362 -2.566489362x + x2 = -0.6941489362 The x term is -2.566489362x. Take half its coefficient (-1.283244681). Square it (1.646716911) and add it to both sides. Add '1.646716911' to each side of the equation. -2.566489362x + 1.646716911 + x2 = -0.6941489362 + 1.646716911 Reorder the terms: 1.646716911 + -2.566489362x + x2 = -0.6941489362 + 1.646716911 Combine like terms: -0.6941489362 + 1.646716911 = 0.9525679748 1.646716911 + -2.566489362x + x2 = 0.9525679748 Factor a perfect square on the left side: (x + -1.283244681)(x + -1.283244681) = 0.9525679748 Calculate the square root of the right side: 0.975995889 Break this problem into two subproblems by setting (x + -1.283244681) equal to 0.975995889 and -0.975995889.Subproblem 1
x + -1.283244681 = 0.975995889 Simplifying x + -1.283244681 = 0.975995889 Reorder the terms: -1.283244681 + x = 0.975995889 Solving -1.283244681 + x = 0.975995889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.283244681' to each side of the equation. -1.283244681 + 1.283244681 + x = 0.975995889 + 1.283244681 Combine like terms: -1.283244681 + 1.283244681 = 0.000000000 0.000000000 + x = 0.975995889 + 1.283244681 x = 0.975995889 + 1.283244681 Combine like terms: 0.975995889 + 1.283244681 = 2.25924057 x = 2.25924057 Simplifying x = 2.25924057Subproblem 2
x + -1.283244681 = -0.975995889 Simplifying x + -1.283244681 = -0.975995889 Reorder the terms: -1.283244681 + x = -0.975995889 Solving -1.283244681 + x = -0.975995889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.283244681' to each side of the equation. -1.283244681 + 1.283244681 + x = -0.975995889 + 1.283244681 Combine like terms: -1.283244681 + 1.283244681 = 0.000000000 0.000000000 + x = -0.975995889 + 1.283244681 x = -0.975995889 + 1.283244681 Combine like terms: -0.975995889 + 1.283244681 = 0.307248792 x = 0.307248792 Simplifying x = 0.307248792Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.25924057, 0.307248792}
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