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Simplifying (x + 10)(x + -4) = 24 Reorder the terms: (10 + x)(x + -4) = 24 Reorder the terms: (10 + x)(-4 + x) = 24 Multiply (10 + x) * (-4 + x) (10(-4 + x) + x(-4 + x)) = 24 ((-4 * 10 + x * 10) + x(-4 + x)) = 24 ((-40 + 10x) + x(-4 + x)) = 24 (-40 + 10x + (-4 * x + x * x)) = 24 (-40 + 10x + (-4x + x2)) = 24 Combine like terms: 10x + -4x = 6x (-40 + 6x + x2) = 24 Solving -40 + 6x + x2 = 24 Solving for variable 'x'. Reorder the terms: -40 + -24 + 6x + x2 = 24 + -24 Combine like terms: -40 + -24 = -64 -64 + 6x + x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -64 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 6x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 6x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 6x + x2 = 0 + 64 6x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 6x + x2 = 64 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 64 + 9 Reorder the terms: 9 + 6x + x2 = 64 + 9 Combine like terms: 64 + 9 = 73 9 + 6x + x2 = 73 Factor a perfect square on the left side: (x + 3)(x + 3) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + 3) equal to 8.544003745 and -8.544003745.Subproblem 1
x + 3 = 8.544003745 Simplifying x + 3 = 8.544003745 Reorder the terms: 3 + x = 8.544003745 Solving 3 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 8.544003745 + -3 Combine like terms: 3 + -3 = 0 0 + x = 8.544003745 + -3 x = 8.544003745 + -3 Combine like terms: 8.544003745 + -3 = 5.544003745 x = 5.544003745 Simplifying x = 5.544003745Subproblem 2
x + 3 = -8.544003745 Simplifying x + 3 = -8.544003745 Reorder the terms: 3 + x = -8.544003745 Solving 3 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -8.544003745 + -3 Combine like terms: 3 + -3 = 0 0 + x = -8.544003745 + -3 x = -8.544003745 + -3 Combine like terms: -8.544003745 + -3 = -11.544003745 x = -11.544003745 Simplifying x = -11.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.544003745, -11.544003745}
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