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Simplifying 9.8x2 + 8x = 1400 Reorder the terms: 8x + 9.8x2 = 1400 Solving 8x + 9.8x2 = 1400 Solving for variable 'x'. Reorder the terms: -1400 + 8x + 9.8x2 = 1400 + -1400 Combine like terms: 1400 + -1400 = 0 -1400 + 8x + 9.8x2 = 0 Begin completing the square. Divide all terms by 9.8 the coefficient of the squared term: Divide each side by '9.8'. -142.8571429 + 0.8163265306x + x2 = 0 Move the constant term to the right: Add '142.8571429' to each side of the equation. -142.8571429 + 0.8163265306x + 142.8571429 + x2 = 0 + 142.8571429 Reorder the terms: -142.8571429 + 142.8571429 + 0.8163265306x + x2 = 0 + 142.8571429 Combine like terms: -142.8571429 + 142.8571429 = 0.0000000 0.0000000 + 0.8163265306x + x2 = 0 + 142.8571429 0.8163265306x + x2 = 0 + 142.8571429 Combine like terms: 0 + 142.8571429 = 142.8571429 0.8163265306x + x2 = 142.8571429 The x term is 0.8163265306x. Take half its coefficient (0.4081632653). Square it (0.1665972511) and add it to both sides. Add '0.1665972511' to each side of the equation. 0.8163265306x + 0.1665972511 + x2 = 142.8571429 + 0.1665972511 Reorder the terms: 0.1665972511 + 0.8163265306x + x2 = 142.8571429 + 0.1665972511 Combine like terms: 142.8571429 + 0.1665972511 = 143.0237401511 0.1665972511 + 0.8163265306x + x2 = 143.0237401511 Factor a perfect square on the left side: (x + 0.4081632653)(x + 0.4081632653) = 143.0237401511 Calculate the square root of the right side: 11.959253327 Break this problem into two subproblems by setting (x + 0.4081632653) equal to 11.959253327 and -11.959253327.Subproblem 1
x + 0.4081632653 = 11.959253327 Simplifying x + 0.4081632653 = 11.959253327 Reorder the terms: 0.4081632653 + x = 11.959253327 Solving 0.4081632653 + x = 11.959253327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4081632653' to each side of the equation. 0.4081632653 + -0.4081632653 + x = 11.959253327 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + x = 11.959253327 + -0.4081632653 x = 11.959253327 + -0.4081632653 Combine like terms: 11.959253327 + -0.4081632653 = 11.5510900617 x = 11.5510900617 Simplifying x = 11.5510900617Subproblem 2
x + 0.4081632653 = -11.959253327 Simplifying x + 0.4081632653 = -11.959253327 Reorder the terms: 0.4081632653 + x = -11.959253327 Solving 0.4081632653 + x = -11.959253327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4081632653' to each side of the equation. 0.4081632653 + -0.4081632653 + x = -11.959253327 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + x = -11.959253327 + -0.4081632653 x = -11.959253327 + -0.4081632653 Combine like terms: -11.959253327 + -0.4081632653 = -12.3674165923 x = -12.3674165923 Simplifying x = -12.3674165923Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.5510900617, -12.3674165923}
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