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Simplifying 2x2 + 21x + -258 = 0 Reorder the terms: -258 + 21x + 2x2 = 0 Solving -258 + 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'. -129 + 10.5x + x2 = 0 Move the constant term to the right: Add '129' to each side of the equation. -129 + 10.5x + 129 + x2 = 0 + 129 Reorder the terms: -129 + 129 + 10.5x + x2 = 0 + 129 Combine like terms: -129 + 129 = 0 0 + 10.5x + x2 = 0 + 129 10.5x + x2 = 0 + 129 Combine like terms: 0 + 129 = 129 10.5x + x2 = 129 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 = 129 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 129 + 27.5625 Combine like terms: 129 + 27.5625 = 156.5625 27.5625 + 10.5x + x2 = 156.5625 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 156.5625 Calculate the square root of the right side: 12.512493756 Break this problem into two subproblems by setting (x + 5.25) equal to 12.512493756 and -12.512493756.Subproblem 1
x + 5.25 = 12.512493756 Simplifying x + 5.25 = 12.512493756 Reorder the terms: 5.25 + x = 12.512493756 Solving 5.25 + x = 12.512493756 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 = 12.512493756 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 12.512493756 + -5.25 x = 12.512493756 + -5.25 Combine like terms: 12.512493756 + -5.25 = 7.262493756 x = 7.262493756 Simplifying x = 7.262493756Subproblem 2
x + 5.25 = -12.512493756 Simplifying x + 5.25 = -12.512493756 Reorder the terms: 5.25 + x = -12.512493756 Solving 5.25 + x = -12.512493756 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 = -12.512493756 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -12.512493756 + -5.25 x = -12.512493756 + -5.25 Combine like terms: -12.512493756 + -5.25 = -17.762493756 x = -17.762493756 Simplifying x = -17.762493756Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.262493756, -17.762493756}
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