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Simplifying 2x(x + 14) = 5x + 1 Reorder the terms: 2x(14 + x) = 5x + 1 (14 * 2x + x * 2x) = 5x + 1 (28x + 2x2) = 5x + 1 Reorder the terms: 28x + 2x2 = 1 + 5x Solving 28x + 2x2 = 1 + 5x Solving for variable 'x'. Reorder the terms: -1 + 28x + -5x + 2x2 = 1 + 5x + -1 + -5x Combine like terms: 28x + -5x = 23x -1 + 23x + 2x2 = 1 + 5x + -1 + -5x Reorder the terms: -1 + 23x + 2x2 = 1 + -1 + 5x + -5x Combine like terms: 1 + -1 = 0 -1 + 23x + 2x2 = 0 + 5x + -5x -1 + 23x + 2x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -1 + 23x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 11.5x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 11.5x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 11.5x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 11.5x + x2 = 0 + 0.5 11.5x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 11.5x + x2 = 0.5 The x term is 11.5x. Take half its coefficient (5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. 11.5x + 33.0625 + x2 = 0.5 + 33.0625 Reorder the terms: 33.0625 + 11.5x + x2 = 0.5 + 33.0625 Combine like terms: 0.5 + 33.0625 = 33.5625 33.0625 + 11.5x + x2 = 33.5625 Factor a perfect square on the left side: (x + 5.75)(x + 5.75) = 33.5625 Calculate the square root of the right side: 5.793315113 Break this problem into two subproblems by setting (x + 5.75) equal to 5.793315113 and -5.793315113.Subproblem 1
x + 5.75 = 5.793315113 Simplifying x + 5.75 = 5.793315113 Reorder the terms: 5.75 + x = 5.793315113 Solving 5.75 + x = 5.793315113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = 5.793315113 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = 5.793315113 + -5.75 x = 5.793315113 + -5.75 Combine like terms: 5.793315113 + -5.75 = 0.043315113 x = 0.043315113 Simplifying x = 0.043315113Subproblem 2
x + 5.75 = -5.793315113 Simplifying x + 5.75 = -5.793315113 Reorder the terms: 5.75 + x = -5.793315113 Solving 5.75 + x = -5.793315113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = -5.793315113 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = -5.793315113 + -5.75 x = -5.793315113 + -5.75 Combine like terms: -5.793315113 + -5.75 = -11.543315113 x = -11.543315113 Simplifying x = -11.543315113Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.043315113, -11.543315113}
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