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Simplifying x2 + 49x + 14 = 42 Reorder the terms: 14 + 49x + x2 = 42 Solving 14 + 49x + x2 = 42 Solving for variable 'x'. Reorder the terms: 14 + -42 + 49x + x2 = 42 + -42 Combine like terms: 14 + -42 = -28 -28 + 49x + x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -28 + 49x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 49x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 49x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 49x + x2 = 0 + 28 49x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 49x + x2 = 28 The x term is 49x. Take half its coefficient (24.5). Square it (600.25) and add it to both sides. Add '600.25' to each side of the equation. 49x + 600.25 + x2 = 28 + 600.25 Reorder the terms: 600.25 + 49x + x2 = 28 + 600.25 Combine like terms: 28 + 600.25 = 628.25 600.25 + 49x + x2 = 628.25 Factor a perfect square on the left side: (x + 24.5)(x + 24.5) = 628.25 Calculate the square root of the right side: 25.064915719 Break this problem into two subproblems by setting (x + 24.5) equal to 25.064915719 and -25.064915719.Subproblem 1
x + 24.5 = 25.064915719 Simplifying x + 24.5 = 25.064915719 Reorder the terms: 24.5 + x = 25.064915719 Solving 24.5 + x = 25.064915719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + x = 25.064915719 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = 25.064915719 + -24.5 x = 25.064915719 + -24.5 Combine like terms: 25.064915719 + -24.5 = 0.564915719 x = 0.564915719 Simplifying x = 0.564915719Subproblem 2
x + 24.5 = -25.064915719 Simplifying x + 24.5 = -25.064915719 Reorder the terms: 24.5 + x = -25.064915719 Solving 24.5 + x = -25.064915719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + x = -25.064915719 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = -25.064915719 + -24.5 x = -25.064915719 + -24.5 Combine like terms: -25.064915719 + -24.5 = -49.564915719 x = -49.564915719 Simplifying x = -49.564915719Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.564915719, -49.564915719}
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