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Simplifying 0.5 = -4.9x2 + 40x + 3 Reorder the terms: 0.5 = 3 + 40x + -4.9x2 Solving 0.5 = 3 + 40x + -4.9x2 Solving for variable 'x'. Combine like terms: 0.5 + -3 = -2.5 -2.5 + -40x + 4.9x2 = 3 + 40x + -4.9x2 + -3 + -40x + 4.9x2 Reorder the terms: -2.5 + -40x + 4.9x2 = 3 + -3 + 40x + -40x + -4.9x2 + 4.9x2 Combine like terms: 3 + -3 = 0 -2.5 + -40x + 4.9x2 = 0 + 40x + -40x + -4.9x2 + 4.9x2 -2.5 + -40x + 4.9x2 = 40x + -40x + -4.9x2 + 4.9x2 Combine like terms: 40x + -40x = 0 -2.5 + -40x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -2.5 + -40x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -2.5 + -40x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.5102040816 + -8.163265306x + x2 = 0 Move the constant term to the right: Add '0.5102040816' to each side of the equation. -0.5102040816 + -8.163265306x + 0.5102040816 + x2 = 0 + 0.5102040816 Reorder the terms: -0.5102040816 + 0.5102040816 + -8.163265306x + x2 = 0 + 0.5102040816 Combine like terms: -0.5102040816 + 0.5102040816 = 0.0000000000 0.0000000000 + -8.163265306x + x2 = 0 + 0.5102040816 -8.163265306x + x2 = 0 + 0.5102040816 Combine like terms: 0 + 0.5102040816 = 0.5102040816 -8.163265306x + x2 = 0.5102040816 The x term is -8.163265306x. Take half its coefficient (-4.081632653). Square it (16.65972511) and add it to both sides. Add '16.65972511' to each side of the equation. -8.163265306x + 16.65972511 + x2 = 0.5102040816 + 16.65972511 Reorder the terms: 16.65972511 + -8.163265306x + x2 = 0.5102040816 + 16.65972511 Combine like terms: 0.5102040816 + 16.65972511 = 17.1699291916 16.65972511 + -8.163265306x + x2 = 17.1699291916 Factor a perfect square on the left side: (x + -4.081632653)(x + -4.081632653) = 17.1699291916 Calculate the square root of the right side: 4.143661327 Break this problem into two subproblems by setting (x + -4.081632653) equal to 4.143661327 and -4.143661327.Subproblem 1
x + -4.081632653 = 4.143661327 Simplifying x + -4.081632653 = 4.143661327 Reorder the terms: -4.081632653 + x = 4.143661327 Solving -4.081632653 + x = 4.143661327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.081632653' to each side of the equation. -4.081632653 + 4.081632653 + x = 4.143661327 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + x = 4.143661327 + 4.081632653 x = 4.143661327 + 4.081632653 Combine like terms: 4.143661327 + 4.081632653 = 8.22529398 x = 8.22529398 Simplifying x = 8.22529398Subproblem 2
x + -4.081632653 = -4.143661327 Simplifying x + -4.081632653 = -4.143661327 Reorder the terms: -4.081632653 + x = -4.143661327 Solving -4.081632653 + x = -4.143661327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.081632653' to each side of the equation. -4.081632653 + 4.081632653 + x = -4.143661327 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + x = -4.143661327 + 4.081632653 x = -4.143661327 + 4.081632653 Combine like terms: -4.143661327 + 4.081632653 = -0.062028674 x = -0.062028674 Simplifying x = -0.062028674Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.22529398, -0.062028674}
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