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Simplifying x2 + -7x = 99 Reorder the terms: -7x + x2 = 99 Solving -7x + x2 = 99 Solving for variable 'x'. Reorder the terms: -99 + -7x + x2 = 99 + -99 Combine like terms: 99 + -99 = 0 -99 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + -7x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + -7x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + -7x + x2 = 0 + 99 -7x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 -7x + x2 = 99 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 = 99 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 99 + 12.25 Combine like terms: 99 + 12.25 = 111.25 12.25 + -7x + x2 = 111.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 111.25 Calculate the square root of the right side: 10.547511555 Break this problem into two subproblems by setting (x + -3.5) equal to 10.547511555 and -10.547511555.Subproblem 1
x + -3.5 = 10.547511555 Simplifying x + -3.5 = 10.547511555 Reorder the terms: -3.5 + x = 10.547511555 Solving -3.5 + x = 10.547511555 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 = 10.547511555 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 10.547511555 + 3.5 x = 10.547511555 + 3.5 Combine like terms: 10.547511555 + 3.5 = 14.047511555 x = 14.047511555 Simplifying x = 14.047511555Subproblem 2
x + -3.5 = -10.547511555 Simplifying x + -3.5 = -10.547511555 Reorder the terms: -3.5 + x = -10.547511555 Solving -3.5 + x = -10.547511555 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 = -10.547511555 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -10.547511555 + 3.5 x = -10.547511555 + 3.5 Combine like terms: -10.547511555 + 3.5 = -7.047511555 x = -7.047511555 Simplifying x = -7.047511555Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.047511555, -7.047511555}
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