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Simplifying (x + 4)(x + -6) = 432 Reorder the terms: (4 + x)(x + -6) = 432 Reorder the terms: (4 + x)(-6 + x) = 432 Multiply (4 + x) * (-6 + x) (4(-6 + x) + x(-6 + x)) = 432 ((-6 * 4 + x * 4) + x(-6 + x)) = 432 ((-24 + 4x) + x(-6 + x)) = 432 (-24 + 4x + (-6 * x + x * x)) = 432 (-24 + 4x + (-6x + x2)) = 432 Combine like terms: 4x + -6x = -2x (-24 + -2x + x2) = 432 Solving -24 + -2x + x2 = 432 Solving for variable 'x'. Reorder the terms: -24 + -432 + -2x + x2 = 432 + -432 Combine like terms: -24 + -432 = -456 -456 + -2x + x2 = 432 + -432 Combine like terms: 432 + -432 = 0 -456 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '456' to each side of the equation. -456 + -2x + 456 + x2 = 0 + 456 Reorder the terms: -456 + 456 + -2x + x2 = 0 + 456 Combine like terms: -456 + 456 = 0 0 + -2x + x2 = 0 + 456 -2x + x2 = 0 + 456 Combine like terms: 0 + 456 = 456 -2x + x2 = 456 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 456 + 1 Reorder the terms: 1 + -2x + x2 = 456 + 1 Combine like terms: 456 + 1 = 457 1 + -2x + x2 = 457 Factor a perfect square on the left side: (x + -1)(x + -1) = 457 Calculate the square root of the right side: 21.377558326 Break this problem into two subproblems by setting (x + -1) equal to 21.377558326 and -21.377558326.Subproblem 1
x + -1 = 21.377558326 Simplifying x + -1 = 21.377558326 Reorder the terms: -1 + x = 21.377558326 Solving -1 + x = 21.377558326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 21.377558326 + 1 Combine like terms: -1 + 1 = 0 0 + x = 21.377558326 + 1 x = 21.377558326 + 1 Combine like terms: 21.377558326 + 1 = 22.377558326 x = 22.377558326 Simplifying x = 22.377558326Subproblem 2
x + -1 = -21.377558326 Simplifying x + -1 = -21.377558326 Reorder the terms: -1 + x = -21.377558326 Solving -1 + x = -21.377558326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -21.377558326 + 1 Combine like terms: -1 + 1 = 0 0 + x = -21.377558326 + 1 x = -21.377558326 + 1 Combine like terms: -21.377558326 + 1 = -20.377558326 x = -20.377558326 Simplifying x = -20.377558326Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.377558326, -20.377558326}
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