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Simplifying 9.99x2 + 1.35x + -3.30 = 0 Reorder the terms: -3.30 + 1.35x + 9.99x2 = 0 Solving -3.30 + 1.35x + 9.99x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9.99 the coefficient of the squared term: Divide each side by '9.99'. -0.3303303303 + 0.1351351351x + x2 = 0 Move the constant term to the right: Add '0.3303303303' to each side of the equation. -0.3303303303 + 0.1351351351x + 0.3303303303 + x2 = 0 + 0.3303303303 Reorder the terms: -0.3303303303 + 0.3303303303 + 0.1351351351x + x2 = 0 + 0.3303303303 Combine like terms: -0.3303303303 + 0.3303303303 = 0.0000000000 0.0000000000 + 0.1351351351x + x2 = 0 + 0.3303303303 0.1351351351x + x2 = 0 + 0.3303303303 Combine like terms: 0 + 0.3303303303 = 0.3303303303 0.1351351351x + x2 = 0.3303303303 The x term is 0.1351351351x. Take half its coefficient (0.06756756755). Square it (0.004565376185) and add it to both sides. Add '0.004565376185' to each side of the equation. 0.1351351351x + 0.004565376185 + x2 = 0.3303303303 + 0.004565376185 Reorder the terms: 0.004565376185 + 0.1351351351x + x2 = 0.3303303303 + 0.004565376185 Combine like terms: 0.3303303303 + 0.004565376185 = 0.334895706485 0.004565376185 + 0.1351351351x + x2 = 0.334895706485 Factor a perfect square on the left side: (x + 0.06756756755)(x + 0.06756756755) = 0.334895706485 Calculate the square root of the right side: 0.578701742 Break this problem into two subproblems by setting (x + 0.06756756755) equal to 0.578701742 and -0.578701742.Subproblem 1
x + 0.06756756755 = 0.578701742 Simplifying x + 0.06756756755 = 0.578701742 Reorder the terms: 0.06756756755 + x = 0.578701742 Solving 0.06756756755 + x = 0.578701742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06756756755' to each side of the equation. 0.06756756755 + -0.06756756755 + x = 0.578701742 + -0.06756756755 Combine like terms: 0.06756756755 + -0.06756756755 = 0.00000000000 0.00000000000 + x = 0.578701742 + -0.06756756755 x = 0.578701742 + -0.06756756755 Combine like terms: 0.578701742 + -0.06756756755 = 0.51113417445 x = 0.51113417445 Simplifying x = 0.51113417445Subproblem 2
x + 0.06756756755 = -0.578701742 Simplifying x + 0.06756756755 = -0.578701742 Reorder the terms: 0.06756756755 + x = -0.578701742 Solving 0.06756756755 + x = -0.578701742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06756756755' to each side of the equation. 0.06756756755 + -0.06756756755 + x = -0.578701742 + -0.06756756755 Combine like terms: 0.06756756755 + -0.06756756755 = 0.00000000000 0.00000000000 + x = -0.578701742 + -0.06756756755 x = -0.578701742 + -0.06756756755 Combine like terms: -0.578701742 + -0.06756756755 = -0.64626930955 x = -0.64626930955 Simplifying x = -0.64626930955Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.51113417445, -0.64626930955}
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