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Simplifying 2345x + -346 + 446x2 = 3567 Reorder the terms: -346 + 2345x + 446x2 = 3567 Solving -346 + 2345x + 446x2 = 3567 Solving for variable 'x'. Reorder the terms: -346 + -3567 + 2345x + 446x2 = 3567 + -3567 Combine like terms: -346 + -3567 = -3913 -3913 + 2345x + 446x2 = 3567 + -3567 Combine like terms: 3567 + -3567 = 0 -3913 + 2345x + 446x2 = 0 Begin completing the square. Divide all terms by 446 the coefficient of the squared term: Divide each side by '446'. -8.773542601 + 5.257847534x + x2 = 0 Move the constant term to the right: Add '8.773542601' to each side of the equation. -8.773542601 + 5.257847534x + 8.773542601 + x2 = 0 + 8.773542601 Reorder the terms: -8.773542601 + 8.773542601 + 5.257847534x + x2 = 0 + 8.773542601 Combine like terms: -8.773542601 + 8.773542601 = 0.000000000 0.000000000 + 5.257847534x + x2 = 0 + 8.773542601 5.257847534x + x2 = 0 + 8.773542601 Combine like terms: 0 + 8.773542601 = 8.773542601 5.257847534x + x2 = 8.773542601 The x term is 5.257847534x. Take half its coefficient (2.628923767). Square it (6.911240173) and add it to both sides. Add '6.911240173' to each side of the equation. 5.257847534x + 6.911240173 + x2 = 8.773542601 + 6.911240173 Reorder the terms: 6.911240173 + 5.257847534x + x2 = 8.773542601 + 6.911240173 Combine like terms: 8.773542601 + 6.911240173 = 15.684782774 6.911240173 + 5.257847534x + x2 = 15.684782774 Factor a perfect square on the left side: (x + 2.628923767)(x + 2.628923767) = 15.684782774 Calculate the square root of the right side: 3.960401845 Break this problem into two subproblems by setting (x + 2.628923767) equal to 3.960401845 and -3.960401845.Subproblem 1
x + 2.628923767 = 3.960401845 Simplifying x + 2.628923767 = 3.960401845 Reorder the terms: 2.628923767 + x = 3.960401845 Solving 2.628923767 + x = 3.960401845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.628923767' to each side of the equation. 2.628923767 + -2.628923767 + x = 3.960401845 + -2.628923767 Combine like terms: 2.628923767 + -2.628923767 = 0.000000000 0.000000000 + x = 3.960401845 + -2.628923767 x = 3.960401845 + -2.628923767 Combine like terms: 3.960401845 + -2.628923767 = 1.331478078 x = 1.331478078 Simplifying x = 1.331478078Subproblem 2
x + 2.628923767 = -3.960401845 Simplifying x + 2.628923767 = -3.960401845 Reorder the terms: 2.628923767 + x = -3.960401845 Solving 2.628923767 + x = -3.960401845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.628923767' to each side of the equation. 2.628923767 + -2.628923767 + x = -3.960401845 + -2.628923767 Combine like terms: 2.628923767 + -2.628923767 = 0.000000000 0.000000000 + x = -3.960401845 + -2.628923767 x = -3.960401845 + -2.628923767 Combine like terms: -3.960401845 + -2.628923767 = -6.589325612 x = -6.589325612 Simplifying x = -6.589325612Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.331478078, -6.589325612}
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