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Simplifying x2 + 8x = 7600 Reorder the terms: 8x + x2 = 7600 Solving 8x + x2 = 7600 Solving for variable 'x'. Reorder the terms: -7600 + 8x + x2 = 7600 + -7600 Combine like terms: 7600 + -7600 = 0 -7600 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7600' to each side of the equation. -7600 + 8x + 7600 + x2 = 0 + 7600 Reorder the terms: -7600 + 7600 + 8x + x2 = 0 + 7600 Combine like terms: -7600 + 7600 = 0 0 + 8x + x2 = 0 + 7600 8x + x2 = 0 + 7600 Combine like terms: 0 + 7600 = 7600 8x + x2 = 7600 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 7600 + 16 Reorder the terms: 16 + 8x + x2 = 7600 + 16 Combine like terms: 7600 + 16 = 7616 16 + 8x + x2 = 7616 Factor a perfect square on the left side: (x + 4)(x + 4) = 7616 Calculate the square root of the right side: 87.269696917 Break this problem into two subproblems by setting (x + 4) equal to 87.269696917 and -87.269696917.Subproblem 1
x + 4 = 87.269696917 Simplifying x + 4 = 87.269696917 Reorder the terms: 4 + x = 87.269696917 Solving 4 + x = 87.269696917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 87.269696917 + -4 Combine like terms: 4 + -4 = 0 0 + x = 87.269696917 + -4 x = 87.269696917 + -4 Combine like terms: 87.269696917 + -4 = 83.269696917 x = 83.269696917 Simplifying x = 83.269696917Subproblem 2
x + 4 = -87.269696917 Simplifying x + 4 = -87.269696917 Reorder the terms: 4 + x = -87.269696917 Solving 4 + x = -87.269696917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -87.269696917 + -4 Combine like terms: 4 + -4 = 0 0 + x = -87.269696917 + -4 x = -87.269696917 + -4 Combine like terms: -87.269696917 + -4 = -91.269696917 x = -91.269696917 Simplifying x = -91.269696917Solution
The solution to the problem is based on the solutions from the subproblems. x = {83.269696917, -91.269696917}
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