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Simplifying 50 = -4.9x2 + 40x + 89 Reorder the terms: 50 = 89 + 40x + -4.9x2 Solving 50 = 89 + 40x + -4.9x2 Solving for variable 'x'. Combine like terms: 50 + -89 = -39 -39 + -40x + 4.9x2 = 89 + 40x + -4.9x2 + -89 + -40x + 4.9x2 Reorder the terms: -39 + -40x + 4.9x2 = 89 + -89 + 40x + -40x + -4.9x2 + 4.9x2 Combine like terms: 89 + -89 = 0 -39 + -40x + 4.9x2 = 0 + 40x + -40x + -4.9x2 + 4.9x2 -39 + -40x + 4.9x2 = 40x + -40x + -4.9x2 + 4.9x2 Combine like terms: 40x + -40x = 0 -39 + -40x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -39 + -40x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -39 + -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'. -7.959183673 + -8.163265306x + x2 = 0 Move the constant term to the right: Add '7.959183673' to each side of the equation. -7.959183673 + -8.163265306x + 7.959183673 + x2 = 0 + 7.959183673 Reorder the terms: -7.959183673 + 7.959183673 + -8.163265306x + x2 = 0 + 7.959183673 Combine like terms: -7.959183673 + 7.959183673 = 0.000000000 0.000000000 + -8.163265306x + x2 = 0 + 7.959183673 -8.163265306x + x2 = 0 + 7.959183673 Combine like terms: 0 + 7.959183673 = 7.959183673 -8.163265306x + x2 = 7.959183673 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 = 7.959183673 + 16.65972511 Reorder the terms: 16.65972511 + -8.163265306x + x2 = 7.959183673 + 16.65972511 Combine like terms: 7.959183673 + 16.65972511 = 24.618908783 16.65972511 + -8.163265306x + x2 = 24.618908783 Factor a perfect square on the left side: (x + -4.081632653)(x + -4.081632653) = 24.618908783 Calculate the square root of the right side: 4.96174453 Break this problem into two subproblems by setting (x + -4.081632653) equal to 4.96174453 and -4.96174453.Subproblem 1
x + -4.081632653 = 4.96174453 Simplifying x + -4.081632653 = 4.96174453 Reorder the terms: -4.081632653 + x = 4.96174453 Solving -4.081632653 + x = 4.96174453 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 = 4.96174453 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + x = 4.96174453 + 4.081632653 x = 4.96174453 + 4.081632653 Combine like terms: 4.96174453 + 4.081632653 = 9.043377183 x = 9.043377183 Simplifying x = 9.043377183Subproblem 2
x + -4.081632653 = -4.96174453 Simplifying x + -4.081632653 = -4.96174453 Reorder the terms: -4.081632653 + x = -4.96174453 Solving -4.081632653 + x = -4.96174453 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 = -4.96174453 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + x = -4.96174453 + 4.081632653 x = -4.96174453 + 4.081632653 Combine like terms: -4.96174453 + 4.081632653 = -0.880111877 x = -0.880111877 Simplifying x = -0.880111877Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.043377183, -0.880111877}
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