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Simplifying x2 + 7x + -175 = 0 Reorder the terms: -175 + 7x + x2 = 0 Solving -175 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '175' to each side of the equation. -175 + 7x + 175 + x2 = 0 + 175 Reorder the terms: -175 + 175 + 7x + x2 = 0 + 175 Combine like terms: -175 + 175 = 0 0 + 7x + x2 = 0 + 175 7x + x2 = 0 + 175 Combine like terms: 0 + 175 = 175 7x + x2 = 175 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 = 175 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 175 + 12.25 Combine like terms: 175 + 12.25 = 187.25 12.25 + 7x + x2 = 187.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 187.25 Calculate the square root of the right side: 13.683932183 Break this problem into two subproblems by setting (x + 3.5) equal to 13.683932183 and -13.683932183.Subproblem 1
x + 3.5 = 13.683932183 Simplifying x + 3.5 = 13.683932183 Reorder the terms: 3.5 + x = 13.683932183 Solving 3.5 + x = 13.683932183 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 = 13.683932183 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 13.683932183 + -3.5 x = 13.683932183 + -3.5 Combine like terms: 13.683932183 + -3.5 = 10.183932183 x = 10.183932183 Simplifying x = 10.183932183Subproblem 2
x + 3.5 = -13.683932183 Simplifying x + 3.5 = -13.683932183 Reorder the terms: 3.5 + x = -13.683932183 Solving 3.5 + x = -13.683932183 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 = -13.683932183 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -13.683932183 + -3.5 x = -13.683932183 + -3.5 Combine like terms: -13.683932183 + -3.5 = -17.183932183 x = -17.183932183 Simplifying x = -17.183932183Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.183932183, -17.183932183}
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