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Simplifying 2x2 + -7x + -21 = 0 Reorder the terms: -21 + -7x + 2x2 = 0 Solving -21 + -7x + 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'. -10.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + -3.5x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + -3.5x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + -3.5x + x2 = 0 + 10.5 -3.5x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 -3.5x + x2 = 10.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 10.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 10.5 + 3.0625 Combine like terms: 10.5 + 3.0625 = 13.5625 3.0625 + -3.5x + x2 = 13.5625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (x + -1.75) equal to 3.682729966 and -3.682729966.Subproblem 1
x + -1.75 = 3.682729966 Simplifying x + -1.75 = 3.682729966 Reorder the terms: -1.75 + x = 3.682729966 Solving -1.75 + x = 3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 3.682729966 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 3.682729966 + 1.75 x = 3.682729966 + 1.75 Combine like terms: 3.682729966 + 1.75 = 5.432729966 x = 5.432729966 Simplifying x = 5.432729966Subproblem 2
x + -1.75 = -3.682729966 Simplifying x + -1.75 = -3.682729966 Reorder the terms: -1.75 + x = -3.682729966 Solving -1.75 + x = -3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -3.682729966 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -3.682729966 + 1.75 x = -3.682729966 + 1.75 Combine like terms: -3.682729966 + 1.75 = -1.932729966 x = -1.932729966 Simplifying x = -1.932729966Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.432729966, -1.932729966}
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