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Simplifying x2 + 7x = 81 Reorder the terms: 7x + x2 = 81 Solving 7x + x2 = 81 Solving for variable 'x'. Reorder the terms: -81 + 7x + x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + 7x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + 7x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 7x + x2 = 0 + 81 7x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 7x + x2 = 81 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 81 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 81 + 12.25 Combine like terms: 81 + 12.25 = 93.25 12.25 + 7x + x2 = 93.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 93.25 Calculate the square root of the right side: 9.656603958 Break this problem into two subproblems by setting (x + 3.5) equal to 9.656603958 and -9.656603958.Subproblem 1
x + 3.5 = 9.656603958 Simplifying x + 3.5 = 9.656603958 Reorder the terms: 3.5 + x = 9.656603958 Solving 3.5 + x = 9.656603958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 9.656603958 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 9.656603958 + -3.5 x = 9.656603958 + -3.5 Combine like terms: 9.656603958 + -3.5 = 6.156603958 x = 6.156603958 Simplifying x = 6.156603958Subproblem 2
x + 3.5 = -9.656603958 Simplifying x + 3.5 = -9.656603958 Reorder the terms: 3.5 + x = -9.656603958 Solving 3.5 + x = -9.656603958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -9.656603958 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -9.656603958 + -3.5 x = -9.656603958 + -3.5 Combine like terms: -9.656603958 + -3.5 = -13.156603958 x = -13.156603958 Simplifying x = -13.156603958Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.156603958, -13.156603958}
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