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Simplifying x2 = -7x + -8 Reorder the terms: x2 = -8 + -7x Solving x2 = -8 + -7x Solving for variable 'x'. Reorder the terms: 8 + 7x + x2 = -8 + -7x + 8 + 7x Reorder the terms: 8 + 7x + x2 = -8 + 8 + -7x + 7x Combine like terms: -8 + 8 = 0 8 + 7x + x2 = 0 + -7x + 7x 8 + 7x + x2 = -7x + 7x Combine like terms: -7x + 7x = 0 8 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 7x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 7x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 7x + x2 = 0 + -8 7x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 7x + x2 = -8 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 = -8 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -8 + 12.25 Combine like terms: -8 + 12.25 = 4.25 12.25 + 7x + x2 = 4.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + 3.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + 3.5 = 2.061552813 Simplifying x + 3.5 = 2.061552813 Reorder the terms: 3.5 + x = 2.061552813 Solving 3.5 + x = 2.061552813 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 = 2.061552813 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 2.061552813 + -3.5 x = 2.061552813 + -3.5 Combine like terms: 2.061552813 + -3.5 = -1.438447187 x = -1.438447187 Simplifying x = -1.438447187Subproblem 2
x + 3.5 = -2.061552813 Simplifying x + 3.5 = -2.061552813 Reorder the terms: 3.5 + x = -2.061552813 Solving 3.5 + x = -2.061552813 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 = -2.061552813 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -2.061552813 + -3.5 x = -2.061552813 + -3.5 Combine like terms: -2.061552813 + -3.5 = -5.561552813 x = -5.561552813 Simplifying x = -5.561552813Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.438447187, -5.561552813}
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