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Simplifying -1x2 + 34x + 321 = 0 Reorder the terms: 321 + 34x + -1x2 = 0 Solving 321 + 34x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -321 + -34x + x2 = 0 Move the constant term to the right: Add '321' to each side of the equation. -321 + -34x + 321 + x2 = 0 + 321 Reorder the terms: -321 + 321 + -34x + x2 = 0 + 321 Combine like terms: -321 + 321 = 0 0 + -34x + x2 = 0 + 321 -34x + x2 = 0 + 321 Combine like terms: 0 + 321 = 321 -34x + x2 = 321 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 = 321 + 289 Reorder the terms: 289 + -34x + x2 = 321 + 289 Combine like terms: 321 + 289 = 610 289 + -34x + x2 = 610 Factor a perfect square on the left side: (x + -17)(x + -17) = 610 Calculate the square root of the right side: 24.69817807 Break this problem into two subproblems by setting (x + -17) equal to 24.69817807 and -24.69817807.Subproblem 1
x + -17 = 24.69817807 Simplifying x + -17 = 24.69817807 Reorder the terms: -17 + x = 24.69817807 Solving -17 + x = 24.69817807 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 = 24.69817807 + 17 Combine like terms: -17 + 17 = 0 0 + x = 24.69817807 + 17 x = 24.69817807 + 17 Combine like terms: 24.69817807 + 17 = 41.69817807 x = 41.69817807 Simplifying x = 41.69817807Subproblem 2
x + -17 = -24.69817807 Simplifying x + -17 = -24.69817807 Reorder the terms: -17 + x = -24.69817807 Solving -17 + x = -24.69817807 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 = -24.69817807 + 17 Combine like terms: -17 + 17 = 0 0 + x = -24.69817807 + 17 x = -24.69817807 + 17 Combine like terms: -24.69817807 + 17 = -7.69817807 x = -7.69817807 Simplifying x = -7.69817807Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.69817807, -7.69817807}
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