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Simplifying x2 + -14x + 49 = 4x + 5 Reorder the terms: 49 + -14x + x2 = 4x + 5 Reorder the terms: 49 + -14x + x2 = 5 + 4x Solving 49 + -14x + x2 = 5 + 4x Solving for variable 'x'. Reorder the terms: 49 + -5 + -14x + -4x + x2 = 5 + 4x + -5 + -4x Combine like terms: 49 + -5 = 44 44 + -14x + -4x + x2 = 5 + 4x + -5 + -4x Combine like terms: -14x + -4x = -18x 44 + -18x + x2 = 5 + 4x + -5 + -4x Reorder the terms: 44 + -18x + x2 = 5 + -5 + 4x + -4x Combine like terms: 5 + -5 = 0 44 + -18x + x2 = 0 + 4x + -4x 44 + -18x + x2 = 4x + -4x Combine like terms: 4x + -4x = 0 44 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-44' to each side of the equation. 44 + -18x + -44 + x2 = 0 + -44 Reorder the terms: 44 + -44 + -18x + x2 = 0 + -44 Combine like terms: 44 + -44 = 0 0 + -18x + x2 = 0 + -44 -18x + x2 = 0 + -44 Combine like terms: 0 + -44 = -44 -18x + x2 = -44 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -44 + 81 Reorder the terms: 81 + -18x + x2 = -44 + 81 Combine like terms: -44 + 81 = 37 81 + -18x + x2 = 37 Factor a perfect square on the left side: (x + -9)(x + -9) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x + -9) equal to 6.08276253 and -6.08276253.Subproblem 1
x + -9 = 6.08276253 Simplifying x + -9 = 6.08276253 Reorder the terms: -9 + x = 6.08276253 Solving -9 + x = 6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 6.08276253 + 9 Combine like terms: -9 + 9 = 0 0 + x = 6.08276253 + 9 x = 6.08276253 + 9 Combine like terms: 6.08276253 + 9 = 15.08276253 x = 15.08276253 Simplifying x = 15.08276253Subproblem 2
x + -9 = -6.08276253 Simplifying x + -9 = -6.08276253 Reorder the terms: -9 + x = -6.08276253 Solving -9 + x = -6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -6.08276253 + 9 Combine like terms: -9 + 9 = 0 0 + x = -6.08276253 + 9 x = -6.08276253 + 9 Combine like terms: -6.08276253 + 9 = 2.91723747 x = 2.91723747 Simplifying x = 2.91723747Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.08276253, 2.91723747}
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