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Simplifying x2 + -35x + -196 = 0 Reorder the terms: -196 + -35x + x2 = 0 Solving -196 + -35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '196' to each side of the equation. -196 + -35x + 196 + x2 = 0 + 196 Reorder the terms: -196 + 196 + -35x + x2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + -35x + x2 = 0 + 196 -35x + x2 = 0 + 196 Combine like terms: 0 + 196 = 196 -35x + x2 = 196 The x term is -35x. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35x + 306.25 + x2 = 196 + 306.25 Reorder the terms: 306.25 + -35x + x2 = 196 + 306.25 Combine like terms: 196 + 306.25 = 502.25 306.25 + -35x + x2 = 502.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 502.25 Calculate the square root of the right side: 22.410934831 Break this problem into two subproblems by setting (x + -17.5) equal to 22.410934831 and -22.410934831.Subproblem 1
x + -17.5 = 22.410934831 Simplifying x + -17.5 = 22.410934831 Reorder the terms: -17.5 + x = 22.410934831 Solving -17.5 + x = 22.410934831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = 22.410934831 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 22.410934831 + 17.5 x = 22.410934831 + 17.5 Combine like terms: 22.410934831 + 17.5 = 39.910934831 x = 39.910934831 Simplifying x = 39.910934831Subproblem 2
x + -17.5 = -22.410934831 Simplifying x + -17.5 = -22.410934831 Reorder the terms: -17.5 + x = -22.410934831 Solving -17.5 + x = -22.410934831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = -22.410934831 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -22.410934831 + 17.5 x = -22.410934831 + 17.5 Combine like terms: -22.410934831 + 17.5 = -4.910934831 x = -4.910934831 Simplifying x = -4.910934831Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.910934831, -4.910934831}
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