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Simplifying 3x + 2x2 + -208 = 0 Reorder the terms: -208 + 3x + 2x2 = 0 Solving -208 + 3x + 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'. -104 + 1.5x + x2 = 0 Move the constant term to the right: Add '104' to each side of the equation. -104 + 1.5x + 104 + x2 = 0 + 104 Reorder the terms: -104 + 104 + 1.5x + x2 = 0 + 104 Combine like terms: -104 + 104 = 0 0 + 1.5x + x2 = 0 + 104 1.5x + x2 = 0 + 104 Combine like terms: 0 + 104 = 104 1.5x + x2 = 104 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 104 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 104 + 0.5625 Combine like terms: 104 + 0.5625 = 104.5625 0.5625 + 1.5x + x2 = 104.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 104.5625 Calculate the square root of the right side: 10.225580668 Break this problem into two subproblems by setting (x + 0.75) equal to 10.225580668 and -10.225580668.Subproblem 1
x + 0.75 = 10.225580668 Simplifying x + 0.75 = 10.225580668 Reorder the terms: 0.75 + x = 10.225580668 Solving 0.75 + x = 10.225580668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 10.225580668 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 10.225580668 + -0.75 x = 10.225580668 + -0.75 Combine like terms: 10.225580668 + -0.75 = 9.475580668 x = 9.475580668 Simplifying x = 9.475580668Subproblem 2
x + 0.75 = -10.225580668 Simplifying x + 0.75 = -10.225580668 Reorder the terms: 0.75 + x = -10.225580668 Solving 0.75 + x = -10.225580668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -10.225580668 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -10.225580668 + -0.75 x = -10.225580668 + -0.75 Combine like terms: -10.225580668 + -0.75 = -10.975580668 x = -10.975580668 Simplifying x = -10.975580668Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.475580668, -10.975580668}
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