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Simplifying 5x(2x + 5) = 19 Reorder the terms: 5x(5 + 2x) = 19 (5 * 5x + 2x * 5x) = 19 (25x + 10x2) = 19 Solving 25x + 10x2 = 19 Solving for variable 'x'. Reorder the terms: -19 + 25x + 10x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + 25x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.9 + 2.5x + x2 = 0.0 Move the constant term to the right: Add '1.9' to each side of the equation. -1.9 + 2.5x + 1.9 + x2 = 0.0 + 1.9 Reorder the terms: -1.9 + 1.9 + 2.5x + x2 = 0.0 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + 2.5x + x2 = 0.0 + 1.9 2.5x + x2 = 0.0 + 1.9 Combine like terms: 0.0 + 1.9 = 1.9 2.5x + x2 = 1.9 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 1.9 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 1.9 + 1.5625 Combine like terms: 1.9 + 1.5625 = 3.4625 1.5625 + 2.5x + x2 = 3.4625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 3.4625 Calculate the square root of the right side: 1.860779407 Break this problem into two subproblems by setting (x + 1.25) equal to 1.860779407 and -1.860779407.Subproblem 1
x + 1.25 = 1.860779407 Simplifying x + 1.25 = 1.860779407 Reorder the terms: 1.25 + x = 1.860779407 Solving 1.25 + x = 1.860779407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.860779407 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.860779407 + -1.25 x = 1.860779407 + -1.25 Combine like terms: 1.860779407 + -1.25 = 0.610779407 x = 0.610779407 Simplifying x = 0.610779407Subproblem 2
x + 1.25 = -1.860779407 Simplifying x + 1.25 = -1.860779407 Reorder the terms: 1.25 + x = -1.860779407 Solving 1.25 + x = -1.860779407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.860779407 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.860779407 + -1.25 x = -1.860779407 + -1.25 Combine like terms: -1.860779407 + -1.25 = -3.110779407 x = -3.110779407 Simplifying x = -3.110779407Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.610779407, -3.110779407}
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