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Simplifying x2 + 35.4x + -355.03 = 0 Reorder the terms: -355.03 + 35.4x + x2 = 0 Solving -355.03 + 35.4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '355.03' to each side of the equation. -355.03 + 35.4x + 355.03 + x2 = 0 + 355.03 Reorder the terms: -355.03 + 355.03 + 35.4x + x2 = 0 + 355.03 Combine like terms: -355.03 + 355.03 = 0.00 0.00 + 35.4x + x2 = 0 + 355.03 35.4x + x2 = 0 + 355.03 Combine like terms: 0 + 355.03 = 355.03 35.4x + x2 = 355.03 The x term is 35.4x. Take half its coefficient (17.7). Square it (313.29) and add it to both sides. Add '313.29' to each side of the equation. 35.4x + 313.29 + x2 = 355.03 + 313.29 Reorder the terms: 313.29 + 35.4x + x2 = 355.03 + 313.29 Combine like terms: 355.03 + 313.29 = 668.32 313.29 + 35.4x + x2 = 668.32 Factor a perfect square on the left side: (x + 17.7)(x + 17.7) = 668.32 Calculate the square root of the right side: 25.851885811 Break this problem into two subproblems by setting (x + 17.7) equal to 25.851885811 and -25.851885811.Subproblem 1
x + 17.7 = 25.851885811 Simplifying x + 17.7 = 25.851885811 Reorder the terms: 17.7 + x = 25.851885811 Solving 17.7 + x = 25.851885811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.7' to each side of the equation. 17.7 + -17.7 + x = 25.851885811 + -17.7 Combine like terms: 17.7 + -17.7 = 0.0 0.0 + x = 25.851885811 + -17.7 x = 25.851885811 + -17.7 Combine like terms: 25.851885811 + -17.7 = 8.151885811 x = 8.151885811 Simplifying x = 8.151885811Subproblem 2
x + 17.7 = -25.851885811 Simplifying x + 17.7 = -25.851885811 Reorder the terms: 17.7 + x = -25.851885811 Solving 17.7 + x = -25.851885811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.7' to each side of the equation. 17.7 + -17.7 + x = -25.851885811 + -17.7 Combine like terms: 17.7 + -17.7 = 0.0 0.0 + x = -25.851885811 + -17.7 x = -25.851885811 + -17.7 Combine like terms: -25.851885811 + -17.7 = -43.551885811 x = -43.551885811 Simplifying x = -43.551885811Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.151885811, -43.551885811}
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