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Simplifying x2 + 4x + -175 = 175 Reorder the terms: -175 + 4x + x2 = 175 Solving -175 + 4x + x2 = 175 Solving for variable 'x'. Reorder the terms: -175 + -175 + 4x + x2 = 175 + -175 Combine like terms: -175 + -175 = -350 -350 + 4x + x2 = 175 + -175 Combine like terms: 175 + -175 = 0 -350 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '350' to each side of the equation. -350 + 4x + 350 + x2 = 0 + 350 Reorder the terms: -350 + 350 + 4x + x2 = 0 + 350 Combine like terms: -350 + 350 = 0 0 + 4x + x2 = 0 + 350 4x + x2 = 0 + 350 Combine like terms: 0 + 350 = 350 4x + x2 = 350 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 350 + 4 Reorder the terms: 4 + 4x + x2 = 350 + 4 Combine like terms: 350 + 4 = 354 4 + 4x + x2 = 354 Factor a perfect square on the left side: (x + 2)(x + 2) = 354 Calculate the square root of the right side: 18.814887722 Break this problem into two subproblems by setting (x + 2) equal to 18.814887722 and -18.814887722.Subproblem 1
x + 2 = 18.814887722 Simplifying x + 2 = 18.814887722 Reorder the terms: 2 + x = 18.814887722 Solving 2 + x = 18.814887722 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 18.814887722 + -2 Combine like terms: 2 + -2 = 0 0 + x = 18.814887722 + -2 x = 18.814887722 + -2 Combine like terms: 18.814887722 + -2 = 16.814887722 x = 16.814887722 Simplifying x = 16.814887722Subproblem 2
x + 2 = -18.814887722 Simplifying x + 2 = -18.814887722 Reorder the terms: 2 + x = -18.814887722 Solving 2 + x = -18.814887722 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -18.814887722 + -2 Combine like terms: 2 + -2 = 0 0 + x = -18.814887722 + -2 x = -18.814887722 + -2 Combine like terms: -18.814887722 + -2 = -20.814887722 x = -20.814887722 Simplifying x = -20.814887722Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.814887722, -20.814887722}
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