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Simplifying x2 + 10x + 21 = 784 Reorder the terms: 21 + 10x + x2 = 784 Solving 21 + 10x + x2 = 784 Solving for variable 'x'. Reorder the terms: 21 + -784 + 10x + x2 = 784 + -784 Combine like terms: 21 + -784 = -763 -763 + 10x + x2 = 784 + -784 Combine like terms: 784 + -784 = 0 -763 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '763' to each side of the equation. -763 + 10x + 763 + x2 = 0 + 763 Reorder the terms: -763 + 763 + 10x + x2 = 0 + 763 Combine like terms: -763 + 763 = 0 0 + 10x + x2 = 0 + 763 10x + x2 = 0 + 763 Combine like terms: 0 + 763 = 763 10x + x2 = 763 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 763 + 25 Reorder the terms: 25 + 10x + x2 = 763 + 25 Combine like terms: 763 + 25 = 788 25 + 10x + x2 = 788 Factor a perfect square on the left side: (x + 5)(x + 5) = 788 Calculate the square root of the right side: 28.071337695 Break this problem into two subproblems by setting (x + 5) equal to 28.071337695 and -28.071337695.Subproblem 1
x + 5 = 28.071337695 Simplifying x + 5 = 28.071337695 Reorder the terms: 5 + x = 28.071337695 Solving 5 + x = 28.071337695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 28.071337695 + -5 Combine like terms: 5 + -5 = 0 0 + x = 28.071337695 + -5 x = 28.071337695 + -5 Combine like terms: 28.071337695 + -5 = 23.071337695 x = 23.071337695 Simplifying x = 23.071337695Subproblem 2
x + 5 = -28.071337695 Simplifying x + 5 = -28.071337695 Reorder the terms: 5 + x = -28.071337695 Solving 5 + x = -28.071337695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -28.071337695 + -5 Combine like terms: 5 + -5 = 0 0 + x = -28.071337695 + -5 x = -28.071337695 + -5 Combine like terms: -28.071337695 + -5 = -33.071337695 x = -33.071337695 Simplifying x = -33.071337695Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.071337695, -33.071337695}
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