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Simplifying x2 + -20x + -97 = 0 Reorder the terms: -97 + -20x + x2 = 0 Solving -97 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '97' to each side of the equation. -97 + -20x + 97 + x2 = 0 + 97 Reorder the terms: -97 + 97 + -20x + x2 = 0 + 97 Combine like terms: -97 + 97 = 0 0 + -20x + x2 = 0 + 97 -20x + x2 = 0 + 97 Combine like terms: 0 + 97 = 97 -20x + x2 = 97 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 97 + 100 Reorder the terms: 100 + -20x + x2 = 97 + 100 Combine like terms: 97 + 100 = 197 100 + -20x + x2 = 197 Factor a perfect square on the left side: (x + -10)(x + -10) = 197 Calculate the square root of the right side: 14.035668848 Break this problem into two subproblems by setting (x + -10) equal to 14.035668848 and -14.035668848.Subproblem 1
x + -10 = 14.035668848 Simplifying x + -10 = 14.035668848 Reorder the terms: -10 + x = 14.035668848 Solving -10 + x = 14.035668848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 14.035668848 + 10 Combine like terms: -10 + 10 = 0 0 + x = 14.035668848 + 10 x = 14.035668848 + 10 Combine like terms: 14.035668848 + 10 = 24.035668848 x = 24.035668848 Simplifying x = 24.035668848Subproblem 2
x + -10 = -14.035668848 Simplifying x + -10 = -14.035668848 Reorder the terms: -10 + x = -14.035668848 Solving -10 + x = -14.035668848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -14.035668848 + 10 Combine like terms: -10 + 10 = 0 0 + x = -14.035668848 + 10 x = -14.035668848 + 10 Combine like terms: -14.035668848 + 10 = -4.035668848 x = -4.035668848 Simplifying x = -4.035668848Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.035668848, -4.035668848}
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