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Simplifying 2x2 + -21x + -178 = 0 Reorder the terms: -178 + -21x + 2x2 = 0 Solving -178 + -21x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -89 + -10.5x + x2 = 0 Move the constant term to the right: Add '89' to each side of the equation. -89 + -10.5x + 89 + x2 = 0 + 89 Reorder the terms: -89 + 89 + -10.5x + x2 = 0 + 89 Combine like terms: -89 + 89 = 0 0 + -10.5x + x2 = 0 + 89 -10.5x + x2 = 0 + 89 Combine like terms: 0 + 89 = 89 -10.5x + x2 = 89 The x term is -10.5x. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5x + 27.5625 + x2 = 89 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = 89 + 27.5625 Combine like terms: 89 + 27.5625 = 116.5625 27.5625 + -10.5x + x2 = 116.5625 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 116.5625 Calculate the square root of the right side: 10.796411441 Break this problem into two subproblems by setting (x + -5.25) equal to 10.796411441 and -10.796411441.Subproblem 1
x + -5.25 = 10.796411441 Simplifying x + -5.25 = 10.796411441 Reorder the terms: -5.25 + x = 10.796411441 Solving -5.25 + x = 10.796411441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 10.796411441 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 10.796411441 + 5.25 x = 10.796411441 + 5.25 Combine like terms: 10.796411441 + 5.25 = 16.046411441 x = 16.046411441 Simplifying x = 16.046411441Subproblem 2
x + -5.25 = -10.796411441 Simplifying x + -5.25 = -10.796411441 Reorder the terms: -5.25 + x = -10.796411441 Solving -5.25 + x = -10.796411441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -10.796411441 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -10.796411441 + 5.25 x = -10.796411441 + 5.25 Combine like terms: -10.796411441 + 5.25 = -5.546411441 x = -5.546411441 Simplifying x = -5.546411441Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.046411441, -5.546411441}
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