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Simplifying -2.08x2 + 77.86x + 1376058 = 0 Reorder the terms: 1376058 + 77.86x + -2.08x2 = 0 Solving 1376058 + 77.86x + -2.08x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2.08 the coefficient of the squared term: Divide each side by '-2.08'. -661566.3462 + -37.43269231x + x2 = 0 Move the constant term to the right: Add '661566.3462' to each side of the equation. -661566.3462 + -37.43269231x + 661566.3462 + x2 = 0 + 661566.3462 Reorder the terms: -661566.3462 + 661566.3462 + -37.43269231x + x2 = 0 + 661566.3462 Combine like terms: -661566.3462 + 661566.3462 = 0.0000 0.0000 + -37.43269231x + x2 = 0 + 661566.3462 -37.43269231x + x2 = 0 + 661566.3462 Combine like terms: 0 + 661566.3462 = 661566.3462 -37.43269231x + x2 = 661566.3462 The x term is -37.43269231x. Take half its coefficient (-18.71634616). Square it (350.3016136) and add it to both sides. Add '350.3016136' to each side of the equation. -37.43269231x + 350.3016136 + x2 = 661566.3462 + 350.3016136 Reorder the terms: 350.3016136 + -37.43269231x + x2 = 661566.3462 + 350.3016136 Combine like terms: 661566.3462 + 350.3016136 = 661916.6478136 350.3016136 + -37.43269231x + x2 = 661916.6478136 Factor a perfect square on the left side: (x + -18.71634616)(x + -18.71634616) = 661916.6478136 Calculate the square root of the right side: 813.582600486 Break this problem into two subproblems by setting (x + -18.71634616) equal to 813.582600486 and -813.582600486.Subproblem 1
x + -18.71634616 = 813.582600486 Simplifying x + -18.71634616 = 813.582600486 Reorder the terms: -18.71634616 + x = 813.582600486 Solving -18.71634616 + x = 813.582600486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.71634616' to each side of the equation. -18.71634616 + 18.71634616 + x = 813.582600486 + 18.71634616 Combine like terms: -18.71634616 + 18.71634616 = 0.00000000 0.00000000 + x = 813.582600486 + 18.71634616 x = 813.582600486 + 18.71634616 Combine like terms: 813.582600486 + 18.71634616 = 832.298946646 x = 832.298946646 Simplifying x = 832.298946646Subproblem 2
x + -18.71634616 = -813.582600486 Simplifying x + -18.71634616 = -813.582600486 Reorder the terms: -18.71634616 + x = -813.582600486 Solving -18.71634616 + x = -813.582600486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.71634616' to each side of the equation. -18.71634616 + 18.71634616 + x = -813.582600486 + 18.71634616 Combine like terms: -18.71634616 + 18.71634616 = 0.00000000 0.00000000 + x = -813.582600486 + 18.71634616 x = -813.582600486 + 18.71634616 Combine like terms: -813.582600486 + 18.71634616 = -794.866254326 x = -794.866254326 Simplifying x = -794.866254326Solution
The solution to the problem is based on the solutions from the subproblems. x = {832.298946646, -794.866254326}
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