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Simplifying x2 + 7x + -187 = 0 Reorder the terms: -187 + 7x + x2 = 0 Solving -187 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '187' to each side of the equation. -187 + 7x + 187 + x2 = 0 + 187 Reorder the terms: -187 + 187 + 7x + x2 = 0 + 187 Combine like terms: -187 + 187 = 0 0 + 7x + x2 = 0 + 187 7x + x2 = 0 + 187 Combine like terms: 0 + 187 = 187 7x + x2 = 187 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 = 187 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 187 + 12.25 Combine like terms: 187 + 12.25 = 199.25 12.25 + 7x + x2 = 199.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 199.25 Calculate the square root of the right side: 14.115594213 Break this problem into two subproblems by setting (x + 3.5) equal to 14.115594213 and -14.115594213.Subproblem 1
x + 3.5 = 14.115594213 Simplifying x + 3.5 = 14.115594213 Reorder the terms: 3.5 + x = 14.115594213 Solving 3.5 + x = 14.115594213 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 = 14.115594213 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 14.115594213 + -3.5 x = 14.115594213 + -3.5 Combine like terms: 14.115594213 + -3.5 = 10.615594213 x = 10.615594213 Simplifying x = 10.615594213Subproblem 2
x + 3.5 = -14.115594213 Simplifying x + 3.5 = -14.115594213 Reorder the terms: 3.5 + x = -14.115594213 Solving 3.5 + x = -14.115594213 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 = -14.115594213 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -14.115594213 + -3.5 x = -14.115594213 + -3.5 Combine like terms: -14.115594213 + -3.5 = -17.615594213 x = -17.615594213 Simplifying x = -17.615594213Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.615594213, -17.615594213}
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