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Simplifying 2x2 + -7x + -50 = 0 Reorder the terms: -50 + -7x + 2x2 = 0 Solving -50 + -7x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -25 + -3.5x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -3.5x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -3.5x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -3.5x + x2 = 0 + 25 -3.5x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -3.5x + x2 = 25 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 25 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 25 + 3.0625 Combine like terms: 25 + 3.0625 = 28.0625 3.0625 + -3.5x + x2 = 28.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 28.0625 Calculate the square root of the right side: 5.297405025 Break this problem into two subproblems by setting (x + -1.75) equal to 5.297405025 and -5.297405025.Subproblem 1
x + -1.75 = 5.297405025 Simplifying x + -1.75 = 5.297405025 Reorder the terms: -1.75 + x = 5.297405025 Solving -1.75 + x = 5.297405025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 5.297405025 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 5.297405025 + 1.75 x = 5.297405025 + 1.75 Combine like terms: 5.297405025 + 1.75 = 7.047405025 x = 7.047405025 Simplifying x = 7.047405025Subproblem 2
x + -1.75 = -5.297405025 Simplifying x + -1.75 = -5.297405025 Reorder the terms: -1.75 + x = -5.297405025 Solving -1.75 + x = -5.297405025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -5.297405025 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -5.297405025 + 1.75 x = -5.297405025 + 1.75 Combine like terms: -5.297405025 + 1.75 = -3.547405025 x = -3.547405025 Simplifying x = -3.547405025Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.047405025, -3.547405025}
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