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Simplifying (x + -4)(x + -10) = 24x Reorder the terms: (-4 + x)(x + -10) = 24x Reorder the terms: (-4 + x)(-10 + x) = 24x Multiply (-4 + x) * (-10 + x) (-4(-10 + x) + x(-10 + x)) = 24x ((-10 * -4 + x * -4) + x(-10 + x)) = 24x ((40 + -4x) + x(-10 + x)) = 24x (40 + -4x + (-10 * x + x * x)) = 24x (40 + -4x + (-10x + x2)) = 24x Combine like terms: -4x + -10x = -14x (40 + -14x + x2) = 24x Solving 40 + -14x + x2 = 24x Solving for variable 'x'. Reorder the terms: 40 + -14x + -24x + x2 = 24x + -24x Combine like terms: -14x + -24x = -38x 40 + -38x + x2 = 24x + -24x Combine like terms: 24x + -24x = 0 40 + -38x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -38x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -38x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -38x + x2 = 0 + -40 -38x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -38x + x2 = -40 The x term is -38x. Take half its coefficient (-19). Square it (361) and add it to both sides. Add '361' to each side of the equation. -38x + 361 + x2 = -40 + 361 Reorder the terms: 361 + -38x + x2 = -40 + 361 Combine like terms: -40 + 361 = 321 361 + -38x + x2 = 321 Factor a perfect square on the left side: (x + -19)(x + -19) = 321 Calculate the square root of the right side: 17.916472867 Break this problem into two subproblems by setting (x + -19) equal to 17.916472867 and -17.916472867.Subproblem 1
x + -19 = 17.916472867 Simplifying x + -19 = 17.916472867 Reorder the terms: -19 + x = 17.916472867 Solving -19 + x = 17.916472867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = 17.916472867 + 19 Combine like terms: -19 + 19 = 0 0 + x = 17.916472867 + 19 x = 17.916472867 + 19 Combine like terms: 17.916472867 + 19 = 36.916472867 x = 36.916472867 Simplifying x = 36.916472867Subproblem 2
x + -19 = -17.916472867 Simplifying x + -19 = -17.916472867 Reorder the terms: -19 + x = -17.916472867 Solving -19 + x = -17.916472867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = -17.916472867 + 19 Combine like terms: -19 + 19 = 0 0 + x = -17.916472867 + 19 x = -17.916472867 + 19 Combine like terms: -17.916472867 + 19 = 1.083527133 x = 1.083527133 Simplifying x = 1.083527133Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.916472867, 1.083527133}
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