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Simplifying x2 + 19x = 174 Reorder the terms: 19x + x2 = 174 Solving 19x + x2 = 174 Solving for variable 'x'. Reorder the terms: -174 + 19x + x2 = 174 + -174 Combine like terms: 174 + -174 = 0 -174 + 19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '174' to each side of the equation. -174 + 19x + 174 + x2 = 0 + 174 Reorder the terms: -174 + 174 + 19x + x2 = 0 + 174 Combine like terms: -174 + 174 = 0 0 + 19x + x2 = 0 + 174 19x + x2 = 0 + 174 Combine like terms: 0 + 174 = 174 19x + x2 = 174 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = 174 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 174 + 90.25 Combine like terms: 174 + 90.25 = 264.25 90.25 + 19x + x2 = 264.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 264.25 Calculate the square root of the right side: 16.255768207 Break this problem into two subproblems by setting (x + 9.5) equal to 16.255768207 and -16.255768207.Subproblem 1
x + 9.5 = 16.255768207 Simplifying x + 9.5 = 16.255768207 Reorder the terms: 9.5 + x = 16.255768207 Solving 9.5 + x = 16.255768207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 16.255768207 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 16.255768207 + -9.5 x = 16.255768207 + -9.5 Combine like terms: 16.255768207 + -9.5 = 6.755768207 x = 6.755768207 Simplifying x = 6.755768207Subproblem 2
x + 9.5 = -16.255768207 Simplifying x + 9.5 = -16.255768207 Reorder the terms: 9.5 + x = -16.255768207 Solving 9.5 + x = -16.255768207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -16.255768207 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -16.255768207 + -9.5 x = -16.255768207 + -9.5 Combine like terms: -16.255768207 + -9.5 = -25.755768207 x = -25.755768207 Simplifying x = -25.755768207Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.755768207, -25.755768207}
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