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Simplifying x2 + -37x + -35 = 0 Reorder the terms: -35 + -37x + x2 = 0 Solving -35 + -37x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -37x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -37x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -37x + x2 = 0 + 35 -37x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -37x + x2 = 35 The x term is -37x. Take half its coefficient (-18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. -37x + 342.25 + x2 = 35 + 342.25 Reorder the terms: 342.25 + -37x + x2 = 35 + 342.25 Combine like terms: 35 + 342.25 = 377.25 342.25 + -37x + x2 = 377.25 Factor a perfect square on the left side: (x + -18.5)(x + -18.5) = 377.25 Calculate the square root of the right side: 19.4229246 Break this problem into two subproblems by setting (x + -18.5) equal to 19.4229246 and -19.4229246.Subproblem 1
x + -18.5 = 19.4229246 Simplifying x + -18.5 = 19.4229246 Reorder the terms: -18.5 + x = 19.4229246 Solving -18.5 + x = 19.4229246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = 19.4229246 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = 19.4229246 + 18.5 x = 19.4229246 + 18.5 Combine like terms: 19.4229246 + 18.5 = 37.9229246 x = 37.9229246 Simplifying x = 37.9229246Subproblem 2
x + -18.5 = -19.4229246 Simplifying x + -18.5 = -19.4229246 Reorder the terms: -18.5 + x = -19.4229246 Solving -18.5 + x = -19.4229246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = -19.4229246 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = -19.4229246 + 18.5 x = -19.4229246 + 18.5 Combine like terms: -19.4229246 + 18.5 = -0.9229246 x = -0.9229246 Simplifying x = -0.9229246Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.9229246, -0.9229246}
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