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Simplifying 25 + -40x = -0.49x2 Solving 25 + -40x = -0.49x2 Solving for variable 'x'. Combine like terms: -0.49x2 + 0.49x2 = 0.00 25 + -40x + 0.49x2 = 0.00 Begin completing the square. Divide all terms by 0.49 the coefficient of the squared term: Divide each side by '0.49'. 51.02040816 + -81.63265306x + x2 = 0 Move the constant term to the right: Add '-51.02040816' to each side of the equation. 51.02040816 + -81.63265306x + -51.02040816 + x2 = 0 + -51.02040816 Reorder the terms: 51.02040816 + -51.02040816 + -81.63265306x + x2 = 0 + -51.02040816 Combine like terms: 51.02040816 + -51.02040816 = 0.00000000 0.00000000 + -81.63265306x + x2 = 0 + -51.02040816 -81.63265306x + x2 = 0 + -51.02040816 Combine like terms: 0 + -51.02040816 = -51.02040816 -81.63265306x + x2 = -51.02040816 The x term is -81.63265306x. Take half its coefficient (-40.81632653). Square it (1665.972511) and add it to both sides. Add '1665.972511' to each side of the equation. -81.63265306x + 1665.972511 + x2 = -51.02040816 + 1665.972511 Reorder the terms: 1665.972511 + -81.63265306x + x2 = -51.02040816 + 1665.972511 Combine like terms: -51.02040816 + 1665.972511 = 1614.95210284 1665.972511 + -81.63265306x + x2 = 1614.95210284 Factor a perfect square on the left side: (x + -40.81632653)(x + -40.81632653) = 1614.95210284 Calculate the square root of the right side: 40.186466663 Break this problem into two subproblems by setting (x + -40.81632653) equal to 40.186466663 and -40.186466663.Subproblem 1
x + -40.81632653 = 40.186466663 Simplifying x + -40.81632653 = 40.186466663 Reorder the terms: -40.81632653 + x = 40.186466663 Solving -40.81632653 + x = 40.186466663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.81632653' to each side of the equation. -40.81632653 + 40.81632653 + x = 40.186466663 + 40.81632653 Combine like terms: -40.81632653 + 40.81632653 = 0.00000000 0.00000000 + x = 40.186466663 + 40.81632653 x = 40.186466663 + 40.81632653 Combine like terms: 40.186466663 + 40.81632653 = 81.002793193 x = 81.002793193 Simplifying x = 81.002793193Subproblem 2
x + -40.81632653 = -40.186466663 Simplifying x + -40.81632653 = -40.186466663 Reorder the terms: -40.81632653 + x = -40.186466663 Solving -40.81632653 + x = -40.186466663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.81632653' to each side of the equation. -40.81632653 + 40.81632653 + x = -40.186466663 + 40.81632653 Combine like terms: -40.81632653 + 40.81632653 = 0.00000000 0.00000000 + x = -40.186466663 + 40.81632653 x = -40.186466663 + 40.81632653 Combine like terms: -40.186466663 + 40.81632653 = 0.629859867 x = 0.629859867 Simplifying x = 0.629859867Solution
The solution to the problem is based on the solutions from the subproblems. x = {81.002793193, 0.629859867}
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