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Simplifying x2 + 7x = -3.25 Reorder the terms: 7x + x2 = -3.25 Solving 7x + x2 = -3.25 Solving for variable 'x'. Reorder the terms: 3.25 + 7x + x2 = -3.25 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 3.25 + 7x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + 7x + -3.25 + x2 = 0.00 + -3.25 Reorder the terms: 3.25 + -3.25 + 7x + x2 = 0.00 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + 7x + x2 = 0.00 + -3.25 7x + x2 = 0.00 + -3.25 Combine like terms: 0.00 + -3.25 = -3.25 7x + x2 = -3.25 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 = -3.25 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -3.25 + 12.25 Combine like terms: -3.25 + 12.25 = 9 12.25 + 7x + x2 = 9 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 9 Calculate the square root of the right side: 3 Break this problem into two subproblems by setting (x + 3.5) equal to 3 and -3.Subproblem 1
x + 3.5 = 3 Simplifying x + 3.5 = 3 Reorder the terms: 3.5 + x = 3 Solving 3.5 + x = 3 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 = 3 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3 + -3.5 x = 3 + -3.5 Combine like terms: 3 + -3.5 = -0.5 x = -0.5 Simplifying x = -0.5Subproblem 2
x + 3.5 = -3 Simplifying x + 3.5 = -3 Reorder the terms: 3.5 + x = -3 Solving 3.5 + x = -3 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 = -3 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3 + -3.5 x = -3 + -3.5 Combine like terms: -3 + -3.5 = -6.5 x = -6.5 Simplifying x = -6.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.5, -6.5}
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