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Simplifying x2 + -24x = -35 Reorder the terms: -24x + x2 = -35 Solving -24x + x2 = -35 Solving for variable 'x'. Reorder the terms: 35 + -24x + x2 = -35 + 35 Combine like terms: -35 + 35 = 0 35 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + -24x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + -24x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -24x + x2 = 0 + -35 -24x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 -24x + x2 = -35 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 = -35 + 144 Reorder the terms: 144 + -24x + x2 = -35 + 144 Combine like terms: -35 + 144 = 109 144 + -24x + x2 = 109 Factor a perfect square on the left side: (x + -12)(x + -12) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (x + -12) equal to 10.440306509 and -10.440306509.Subproblem 1
x + -12 = 10.440306509 Simplifying x + -12 = 10.440306509 Reorder the terms: -12 + x = 10.440306509 Solving -12 + x = 10.440306509 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 = 10.440306509 + 12 Combine like terms: -12 + 12 = 0 0 + x = 10.440306509 + 12 x = 10.440306509 + 12 Combine like terms: 10.440306509 + 12 = 22.440306509 x = 22.440306509 Simplifying x = 22.440306509Subproblem 2
x + -12 = -10.440306509 Simplifying x + -12 = -10.440306509 Reorder the terms: -12 + x = -10.440306509 Solving -12 + x = -10.440306509 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 = -10.440306509 + 12 Combine like terms: -12 + 12 = 0 0 + x = -10.440306509 + 12 x = -10.440306509 + 12 Combine like terms: -10.440306509 + 12 = 1.559693491 x = 1.559693491 Simplifying x = 1.559693491Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.440306509, 1.559693491}
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