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Simplifying x2 + 24x = 170 Reorder the terms: 24x + x2 = 170 Solving 24x + x2 = 170 Solving for variable 'x'. Reorder the terms: -170 + 24x + x2 = 170 + -170 Combine like terms: 170 + -170 = 0 -170 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '170' to each side of the equation. -170 + 24x + 170 + x2 = 0 + 170 Reorder the terms: -170 + 170 + 24x + x2 = 0 + 170 Combine like terms: -170 + 170 = 0 0 + 24x + x2 = 0 + 170 24x + x2 = 0 + 170 Combine like terms: 0 + 170 = 170 24x + x2 = 170 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 170 + 144 Reorder the terms: 144 + 24x + x2 = 170 + 144 Combine like terms: 170 + 144 = 314 144 + 24x + x2 = 314 Factor a perfect square on the left side: (x + 12)(x + 12) = 314 Calculate the square root of the right side: 17.720045147 Break this problem into two subproblems by setting (x + 12) equal to 17.720045147 and -17.720045147.Subproblem 1
x + 12 = 17.720045147 Simplifying x + 12 = 17.720045147 Reorder the terms: 12 + x = 17.720045147 Solving 12 + x = 17.720045147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 17.720045147 + -12 Combine like terms: 12 + -12 = 0 0 + x = 17.720045147 + -12 x = 17.720045147 + -12 Combine like terms: 17.720045147 + -12 = 5.720045147 x = 5.720045147 Simplifying x = 5.720045147Subproblem 2
x + 12 = -17.720045147 Simplifying x + 12 = -17.720045147 Reorder the terms: 12 + x = -17.720045147 Solving 12 + x = -17.720045147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -17.720045147 + -12 Combine like terms: 12 + -12 = 0 0 + x = -17.720045147 + -12 x = -17.720045147 + -12 Combine like terms: -17.720045147 + -12 = -29.720045147 x = -29.720045147 Simplifying x = -29.720045147Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.720045147, -29.720045147}
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