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Simplifying x2 + 7x = 720 Reorder the terms: 7x + x2 = 720 Solving 7x + x2 = 720 Solving for variable 'x'. Reorder the terms: -720 + 7x + x2 = 720 + -720 Combine like terms: 720 + -720 = 0 -720 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '720' to each side of the equation. -720 + 7x + 720 + x2 = 0 + 720 Reorder the terms: -720 + 720 + 7x + x2 = 0 + 720 Combine like terms: -720 + 720 = 0 0 + 7x + x2 = 0 + 720 7x + x2 = 0 + 720 Combine like terms: 0 + 720 = 720 7x + x2 = 720 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 = 720 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 720 + 12.25 Combine like terms: 720 + 12.25 = 732.25 12.25 + 7x + x2 = 732.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 732.25 Calculate the square root of the right side: 27.060118255 Break this problem into two subproblems by setting (x + 3.5) equal to 27.060118255 and -27.060118255.Subproblem 1
x + 3.5 = 27.060118255 Simplifying x + 3.5 = 27.060118255 Reorder the terms: 3.5 + x = 27.060118255 Solving 3.5 + x = 27.060118255 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 = 27.060118255 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 27.060118255 + -3.5 x = 27.060118255 + -3.5 Combine like terms: 27.060118255 + -3.5 = 23.560118255 x = 23.560118255 Simplifying x = 23.560118255Subproblem 2
x + 3.5 = -27.060118255 Simplifying x + 3.5 = -27.060118255 Reorder the terms: 3.5 + x = -27.060118255 Solving 3.5 + x = -27.060118255 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 = -27.060118255 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -27.060118255 + -3.5 x = -27.060118255 + -3.5 Combine like terms: -27.060118255 + -3.5 = -30.560118255 x = -30.560118255 Simplifying x = -30.560118255Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.560118255, -30.560118255}
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