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Simplifying (x + 30)(x + -3) = 40 Reorder the terms: (30 + x)(x + -3) = 40 Reorder the terms: (30 + x)(-3 + x) = 40 Multiply (30 + x) * (-3 + x) (30(-3 + x) + x(-3 + x)) = 40 ((-3 * 30 + x * 30) + x(-3 + x)) = 40 ((-90 + 30x) + x(-3 + x)) = 40 (-90 + 30x + (-3 * x + x * x)) = 40 (-90 + 30x + (-3x + x2)) = 40 Combine like terms: 30x + -3x = 27x (-90 + 27x + x2) = 40 Solving -90 + 27x + x2 = 40 Solving for variable 'x'. Reorder the terms: -90 + -40 + 27x + x2 = 40 + -40 Combine like terms: -90 + -40 = -130 -130 + 27x + x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -130 + 27x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + 27x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + 27x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 27x + x2 = 0 + 130 27x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 27x + x2 = 130 The x term is 27x. Take half its coefficient (13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. 27x + 182.25 + x2 = 130 + 182.25 Reorder the terms: 182.25 + 27x + x2 = 130 + 182.25 Combine like terms: 130 + 182.25 = 312.25 182.25 + 27x + x2 = 312.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 312.25 Calculate the square root of the right side: 17.670597047 Break this problem into two subproblems by setting (x + 13.5) equal to 17.670597047 and -17.670597047.Subproblem 1
x + 13.5 = 17.670597047 Simplifying x + 13.5 = 17.670597047 Reorder the terms: 13.5 + x = 17.670597047 Solving 13.5 + x = 17.670597047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = 17.670597047 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 17.670597047 + -13.5 x = 17.670597047 + -13.5 Combine like terms: 17.670597047 + -13.5 = 4.170597047 x = 4.170597047 Simplifying x = 4.170597047Subproblem 2
x + 13.5 = -17.670597047 Simplifying x + 13.5 = -17.670597047 Reorder the terms: 13.5 + x = -17.670597047 Solving 13.5 + x = -17.670597047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = -17.670597047 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -17.670597047 + -13.5 x = -17.670597047 + -13.5 Combine like terms: -17.670597047 + -13.5 = -31.170597047 x = -31.170597047 Simplifying x = -31.170597047Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.170597047, -31.170597047}
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