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Simplifying x2 + -34x + -4 = 0 Reorder the terms: -4 + -34x + x2 = 0 Solving -4 + -34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -34x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -34x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -34x + x2 = 0 + 4 -34x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -34x + x2 = 4 The x term is -34x. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34x + 289 + x2 = 4 + 289 Reorder the terms: 289 + -34x + x2 = 4 + 289 Combine like terms: 4 + 289 = 293 289 + -34x + x2 = 293 Factor a perfect square on the left side: (x + -17)(x + -17) = 293 Calculate the square root of the right side: 17.117242769 Break this problem into two subproblems by setting (x + -17) equal to 17.117242769 and -17.117242769.Subproblem 1
x + -17 = 17.117242769 Simplifying x + -17 = 17.117242769 Reorder the terms: -17 + x = 17.117242769 Solving -17 + x = 17.117242769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 17.117242769 + 17 Combine like terms: -17 + 17 = 0 0 + x = 17.117242769 + 17 x = 17.117242769 + 17 Combine like terms: 17.117242769 + 17 = 34.117242769 x = 34.117242769 Simplifying x = 34.117242769Subproblem 2
x + -17 = -17.117242769 Simplifying x + -17 = -17.117242769 Reorder the terms: -17 + x = -17.117242769 Solving -17 + x = -17.117242769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = -17.117242769 + 17 Combine like terms: -17 + 17 = 0 0 + x = -17.117242769 + 17 x = -17.117242769 + 17 Combine like terms: -17.117242769 + 17 = -0.117242769 x = -0.117242769 Simplifying x = -0.117242769Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.117242769, -0.117242769}
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