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Simplifying x2 + 16x = 393 Reorder the terms: 16x + x2 = 393 Solving 16x + x2 = 393 Solving for variable 'x'. Reorder the terms: -393 + 16x + x2 = 393 + -393 Combine like terms: 393 + -393 = 0 -393 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '393' to each side of the equation. -393 + 16x + 393 + x2 = 0 + 393 Reorder the terms: -393 + 393 + 16x + x2 = 0 + 393 Combine like terms: -393 + 393 = 0 0 + 16x + x2 = 0 + 393 16x + x2 = 0 + 393 Combine like terms: 0 + 393 = 393 16x + x2 = 393 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 393 + 64 Reorder the terms: 64 + 16x + x2 = 393 + 64 Combine like terms: 393 + 64 = 457 64 + 16x + x2 = 457 Factor a perfect square on the left side: (x + 8)(x + 8) = 457 Calculate the square root of the right side: 21.377558326 Break this problem into two subproblems by setting (x + 8) equal to 21.377558326 and -21.377558326.Subproblem 1
x + 8 = 21.377558326 Simplifying x + 8 = 21.377558326 Reorder the terms: 8 + x = 21.377558326 Solving 8 + x = 21.377558326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 21.377558326 + -8 Combine like terms: 8 + -8 = 0 0 + x = 21.377558326 + -8 x = 21.377558326 + -8 Combine like terms: 21.377558326 + -8 = 13.377558326 x = 13.377558326 Simplifying x = 13.377558326Subproblem 2
x + 8 = -21.377558326 Simplifying x + 8 = -21.377558326 Reorder the terms: 8 + x = -21.377558326 Solving 8 + x = -21.377558326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -21.377558326 + -8 Combine like terms: 8 + -8 = 0 0 + x = -21.377558326 + -8 x = -21.377558326 + -8 Combine like terms: -21.377558326 + -8 = -29.377558326 x = -29.377558326 Simplifying x = -29.377558326Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.377558326, -29.377558326}
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