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Simplifying 2x2 + 7x + 21 + -1x2 + 10x + 25 = 0 Reorder the terms: 21 + 25 + 7x + 10x + 2x2 + -1x2 = 0 Combine like terms: 21 + 25 = 46 46 + 7x + 10x + 2x2 + -1x2 = 0 Combine like terms: 7x + 10x = 17x 46 + 17x + 2x2 + -1x2 = 0 Combine like terms: 2x2 + -1x2 = 1x2 46 + 17x + 1x2 = 0 Solving 46 + 17x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-46' to each side of the equation. 46 + 17x + -46 + x2 = 0 + -46 Reorder the terms: 46 + -46 + 17x + x2 = 0 + -46 Combine like terms: 46 + -46 = 0 0 + 17x + x2 = 0 + -46 17x + x2 = 0 + -46 Combine like terms: 0 + -46 = -46 17x + x2 = -46 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = -46 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -46 + 72.25 Combine like terms: -46 + 72.25 = 26.25 72.25 + 17x + x2 = 26.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (x + 8.5) equal to 5.123475383 and -5.123475383.Subproblem 1
x + 8.5 = 5.123475383 Simplifying x + 8.5 = 5.123475383 Reorder the terms: 8.5 + x = 5.123475383 Solving 8.5 + x = 5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 5.123475383 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 5.123475383 + -8.5 x = 5.123475383 + -8.5 Combine like terms: 5.123475383 + -8.5 = -3.376524617 x = -3.376524617 Simplifying x = -3.376524617Subproblem 2
x + 8.5 = -5.123475383 Simplifying x + 8.5 = -5.123475383 Reorder the terms: 8.5 + x = -5.123475383 Solving 8.5 + x = -5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -5.123475383 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -5.123475383 + -8.5 x = -5.123475383 + -8.5 Combine like terms: -5.123475383 + -8.5 = -13.623475383 x = -13.623475383 Simplifying x = -13.623475383Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.376524617, -13.623475383}
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