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Simplifying x2 + 24x + -74 = 0 Reorder the terms: -74 + 24x + x2 = 0 Solving -74 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + 24x + 74 + x2 = 0 + 74 Reorder the terms: -74 + 74 + 24x + x2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + 24x + x2 = 0 + 74 24x + x2 = 0 + 74 Combine like terms: 0 + 74 = 74 24x + x2 = 74 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 = 74 + 144 Reorder the terms: 144 + 24x + x2 = 74 + 144 Combine like terms: 74 + 144 = 218 144 + 24x + x2 = 218 Factor a perfect square on the left side: (x + 12)(x + 12) = 218 Calculate the square root of the right side: 14.76482306 Break this problem into two subproblems by setting (x + 12) equal to 14.76482306 and -14.76482306.Subproblem 1
x + 12 = 14.76482306 Simplifying x + 12 = 14.76482306 Reorder the terms: 12 + x = 14.76482306 Solving 12 + x = 14.76482306 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 = 14.76482306 + -12 Combine like terms: 12 + -12 = 0 0 + x = 14.76482306 + -12 x = 14.76482306 + -12 Combine like terms: 14.76482306 + -12 = 2.76482306 x = 2.76482306 Simplifying x = 2.76482306Subproblem 2
x + 12 = -14.76482306 Simplifying x + 12 = -14.76482306 Reorder the terms: 12 + x = -14.76482306 Solving 12 + x = -14.76482306 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 = -14.76482306 + -12 Combine like terms: 12 + -12 = 0 0 + x = -14.76482306 + -12 x = -14.76482306 + -12 Combine like terms: -14.76482306 + -12 = -26.76482306 x = -26.76482306 Simplifying x = -26.76482306Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.76482306, -26.76482306}
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