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Simplifying (2x + -5) * x + 2 = 49 Reorder the terms: (-5 + 2x) * x + 2 = 49 Reorder the terms for easier multiplication: x(-5 + 2x) + 2 = 49 (-5 * x + 2x * x) + 2 = 49 (-5x + 2x2) + 2 = 49 Reorder the terms: 2 + -5x + 2x2 = 49 Solving 2 + -5x + 2x2 = 49 Solving for variable 'x'. Reorder the terms: 2 + -49 + -5x + 2x2 = 49 + -49 Combine like terms: 2 + -49 = -47 -47 + -5x + 2x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -47 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -23.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '23.5' to each side of the equation. -23.5 + -2.5x + 23.5 + x2 = 0 + 23.5 Reorder the terms: -23.5 + 23.5 + -2.5x + x2 = 0 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + -2.5x + x2 = 0 + 23.5 -2.5x + x2 = 0 + 23.5 Combine like terms: 0 + 23.5 = 23.5 -2.5x + x2 = 23.5 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 = 23.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 23.5 + 1.5625 Combine like terms: 23.5 + 1.5625 = 25.0625 1.5625 + -2.5x + x2 = 25.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 25.0625 Calculate the square root of the right side: 5.006246099 Break this problem into two subproblems by setting (x + -1.25) equal to 5.006246099 and -5.006246099.Subproblem 1
x + -1.25 = 5.006246099 Simplifying x + -1.25 = 5.006246099 Reorder the terms: -1.25 + x = 5.006246099 Solving -1.25 + x = 5.006246099 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 = 5.006246099 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 5.006246099 + 1.25 x = 5.006246099 + 1.25 Combine like terms: 5.006246099 + 1.25 = 6.256246099 x = 6.256246099 Simplifying x = 6.256246099Subproblem 2
x + -1.25 = -5.006246099 Simplifying x + -1.25 = -5.006246099 Reorder the terms: -1.25 + x = -5.006246099 Solving -1.25 + x = -5.006246099 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 = -5.006246099 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -5.006246099 + 1.25 x = -5.006246099 + 1.25 Combine like terms: -5.006246099 + 1.25 = -3.756246099 x = -3.756246099 Simplifying x = -3.756246099Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.256246099, -3.756246099}
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