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Simplifying 2x2 + 7x + -52 = 0 Reorder the terms: -52 + 7x + 2x2 = 0 Solving -52 + 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'. -26 + 3.5x + x2 = 0 Move the constant term to the right: Add '26' to each side of the equation. -26 + 3.5x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + 3.5x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 3.5x + x2 = 0 + 26 3.5x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 3.5x + x2 = 26 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 = 26 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 26 + 3.0625 Combine like terms: 26 + 3.0625 = 29.0625 3.0625 + 3.5x + x2 = 29.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 29.0625 Calculate the square root of the right side: 5.390964663 Break this problem into two subproblems by setting (x + 1.75) equal to 5.390964663 and -5.390964663.Subproblem 1
x + 1.75 = 5.390964663 Simplifying x + 1.75 = 5.390964663 Reorder the terms: 1.75 + x = 5.390964663 Solving 1.75 + x = 5.390964663 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 = 5.390964663 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 5.390964663 + -1.75 x = 5.390964663 + -1.75 Combine like terms: 5.390964663 + -1.75 = 3.640964663 x = 3.640964663 Simplifying x = 3.640964663Subproblem 2
x + 1.75 = -5.390964663 Simplifying x + 1.75 = -5.390964663 Reorder the terms: 1.75 + x = -5.390964663 Solving 1.75 + x = -5.390964663 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 = -5.390964663 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -5.390964663 + -1.75 x = -5.390964663 + -1.75 Combine like terms: -5.390964663 + -1.75 = -7.140964663 x = -7.140964663 Simplifying x = -7.140964663Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.640964663, -7.140964663}
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