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Simplifying x2 + 7x + -69 = 0 Reorder the terms: -69 + 7x + x2 = 0 Solving -69 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '69' to each side of the equation. -69 + 7x + 69 + x2 = 0 + 69 Reorder the terms: -69 + 69 + 7x + x2 = 0 + 69 Combine like terms: -69 + 69 = 0 0 + 7x + x2 = 0 + 69 7x + x2 = 0 + 69 Combine like terms: 0 + 69 = 69 7x + x2 = 69 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 = 69 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 69 + 12.25 Combine like terms: 69 + 12.25 = 81.25 12.25 + 7x + x2 = 81.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 81.25 Calculate the square root of the right side: 9.013878189 Break this problem into two subproblems by setting (x + 3.5) equal to 9.013878189 and -9.013878189.Subproblem 1
x + 3.5 = 9.013878189 Simplifying x + 3.5 = 9.013878189 Reorder the terms: 3.5 + x = 9.013878189 Solving 3.5 + x = 9.013878189 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 = 9.013878189 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 9.013878189 + -3.5 x = 9.013878189 + -3.5 Combine like terms: 9.013878189 + -3.5 = 5.513878189 x = 5.513878189 Simplifying x = 5.513878189Subproblem 2
x + 3.5 = -9.013878189 Simplifying x + 3.5 = -9.013878189 Reorder the terms: 3.5 + x = -9.013878189 Solving 3.5 + x = -9.013878189 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 = -9.013878189 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -9.013878189 + -3.5 x = -9.013878189 + -3.5 Combine like terms: -9.013878189 + -3.5 = -12.513878189 x = -12.513878189 Simplifying x = -12.513878189Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.513878189, -12.513878189}
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