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Simplifying x2 + -6.5x + -52 = 0 Reorder the terms: -52 + -6.5x + x2 = 0 Solving -52 + -6.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + -6.5x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + -6.5x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -6.5x + x2 = 0 + 52 -6.5x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 -6.5x + x2 = 52 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 52 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 52 + 10.5625 Combine like terms: 52 + 10.5625 = 62.5625 10.5625 + -6.5x + x2 = 62.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 62.5625 Calculate the square root of the right side: 7.90964601 Break this problem into two subproblems by setting (x + -3.25) equal to 7.90964601 and -7.90964601.Subproblem 1
x + -3.25 = 7.90964601 Simplifying x + -3.25 = 7.90964601 Reorder the terms: -3.25 + x = 7.90964601 Solving -3.25 + x = 7.90964601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 7.90964601 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 7.90964601 + 3.25 x = 7.90964601 + 3.25 Combine like terms: 7.90964601 + 3.25 = 11.15964601 x = 11.15964601 Simplifying x = 11.15964601Subproblem 2
x + -3.25 = -7.90964601 Simplifying x + -3.25 = -7.90964601 Reorder the terms: -3.25 + x = -7.90964601 Solving -3.25 + x = -7.90964601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -7.90964601 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -7.90964601 + 3.25 x = -7.90964601 + 3.25 Combine like terms: -7.90964601 + 3.25 = -4.65964601 x = -4.65964601 Simplifying x = -4.65964601Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.15964601, -4.65964601}
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