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Simplifying (x + -6)(x + -8) = 432 Reorder the terms: (-6 + x)(x + -8) = 432 Reorder the terms: (-6 + x)(-8 + x) = 432 Multiply (-6 + x) * (-8 + x) (-6(-8 + x) + x(-8 + x)) = 432 ((-8 * -6 + x * -6) + x(-8 + x)) = 432 ((48 + -6x) + x(-8 + x)) = 432 (48 + -6x + (-8 * x + x * x)) = 432 (48 + -6x + (-8x + x2)) = 432 Combine like terms: -6x + -8x = -14x (48 + -14x + x2) = 432 Solving 48 + -14x + x2 = 432 Solving for variable 'x'. Reorder the terms: 48 + -432 + -14x + x2 = 432 + -432 Combine like terms: 48 + -432 = -384 -384 + -14x + x2 = 432 + -432 Combine like terms: 432 + -432 = 0 -384 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '384' to each side of the equation. -384 + -14x + 384 + x2 = 0 + 384 Reorder the terms: -384 + 384 + -14x + x2 = 0 + 384 Combine like terms: -384 + 384 = 0 0 + -14x + x2 = 0 + 384 -14x + x2 = 0 + 384 Combine like terms: 0 + 384 = 384 -14x + x2 = 384 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 384 + 49 Reorder the terms: 49 + -14x + x2 = 384 + 49 Combine like terms: 384 + 49 = 433 49 + -14x + x2 = 433 Factor a perfect square on the left side: (x + -7)(x + -7) = 433 Calculate the square root of the right side: 20.808652047 Break this problem into two subproblems by setting (x + -7) equal to 20.808652047 and -20.808652047.Subproblem 1
x + -7 = 20.808652047 Simplifying x + -7 = 20.808652047 Reorder the terms: -7 + x = 20.808652047 Solving -7 + x = 20.808652047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 20.808652047 + 7 Combine like terms: -7 + 7 = 0 0 + x = 20.808652047 + 7 x = 20.808652047 + 7 Combine like terms: 20.808652047 + 7 = 27.808652047 x = 27.808652047 Simplifying x = 27.808652047Subproblem 2
x + -7 = -20.808652047 Simplifying x + -7 = -20.808652047 Reorder the terms: -7 + x = -20.808652047 Solving -7 + x = -20.808652047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -20.808652047 + 7 Combine like terms: -7 + 7 = 0 0 + x = -20.808652047 + 7 x = -20.808652047 + 7 Combine like terms: -20.808652047 + 7 = -13.808652047 x = -13.808652047 Simplifying x = -13.808652047Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.808652047, -13.808652047}
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