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Simplifying 22x2 + 5x + -840 = 0 Reorder the terms: -840 + 5x + 22x2 = 0 Solving -840 + 5x + 22x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. -38.18181818 + 0.2272727273x + x2 = 0 Move the constant term to the right: Add '38.18181818' to each side of the equation. -38.18181818 + 0.2272727273x + 38.18181818 + x2 = 0 + 38.18181818 Reorder the terms: -38.18181818 + 38.18181818 + 0.2272727273x + x2 = 0 + 38.18181818 Combine like terms: -38.18181818 + 38.18181818 = 0.00000000 0.00000000 + 0.2272727273x + x2 = 0 + 38.18181818 0.2272727273x + x2 = 0 + 38.18181818 Combine like terms: 0 + 38.18181818 = 38.18181818 0.2272727273x + x2 = 38.18181818 The x term is 0.2272727273x. Take half its coefficient (0.1136363637). Square it (0.01291322316) and add it to both sides. Add '0.01291322316' to each side of the equation. 0.2272727273x + 0.01291322316 + x2 = 38.18181818 + 0.01291322316 Reorder the terms: 0.01291322316 + 0.2272727273x + x2 = 38.18181818 + 0.01291322316 Combine like terms: 38.18181818 + 0.01291322316 = 38.19473140316 0.01291322316 + 0.2272727273x + x2 = 38.19473140316 Factor a perfect square on the left side: (x + 0.1136363637)(x + 0.1136363637) = 38.19473140316 Calculate the square root of the right side: 6.180188622 Break this problem into two subproblems by setting (x + 0.1136363637) equal to 6.180188622 and -6.180188622.Subproblem 1
x + 0.1136363637 = 6.180188622 Simplifying x + 0.1136363637 = 6.180188622 Reorder the terms: 0.1136363637 + x = 6.180188622 Solving 0.1136363637 + x = 6.180188622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1136363637' to each side of the equation. 0.1136363637 + -0.1136363637 + x = 6.180188622 + -0.1136363637 Combine like terms: 0.1136363637 + -0.1136363637 = 0.0000000000 0.0000000000 + x = 6.180188622 + -0.1136363637 x = 6.180188622 + -0.1136363637 Combine like terms: 6.180188622 + -0.1136363637 = 6.0665522583 x = 6.0665522583 Simplifying x = 6.0665522583Subproblem 2
x + 0.1136363637 = -6.180188622 Simplifying x + 0.1136363637 = -6.180188622 Reorder the terms: 0.1136363637 + x = -6.180188622 Solving 0.1136363637 + x = -6.180188622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1136363637' to each side of the equation. 0.1136363637 + -0.1136363637 + x = -6.180188622 + -0.1136363637 Combine like terms: 0.1136363637 + -0.1136363637 = 0.0000000000 0.0000000000 + x = -6.180188622 + -0.1136363637 x = -6.180188622 + -0.1136363637 Combine like terms: -6.180188622 + -0.1136363637 = -6.2938249857 x = -6.2938249857 Simplifying x = -6.2938249857Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.0665522583, -6.2938249857}
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