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Simplifying (x + -3)(x + -5) = 84 Reorder the terms: (-3 + x)(x + -5) = 84 Reorder the terms: (-3 + x)(-5 + x) = 84 Multiply (-3 + x) * (-5 + x) (-3(-5 + x) + x(-5 + x)) = 84 ((-5 * -3 + x * -3) + x(-5 + x)) = 84 ((15 + -3x) + x(-5 + x)) = 84 (15 + -3x + (-5 * x + x * x)) = 84 (15 + -3x + (-5x + x2)) = 84 Combine like terms: -3x + -5x = -8x (15 + -8x + x2) = 84 Solving 15 + -8x + x2 = 84 Solving for variable 'x'. Reorder the terms: 15 + -84 + -8x + x2 = 84 + -84 Combine like terms: 15 + -84 = -69 -69 + -8x + x2 = 84 + -84 Combine like terms: 84 + -84 = 0 -69 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '69' to each side of the equation. -69 + -8x + 69 + x2 = 0 + 69 Reorder the terms: -69 + 69 + -8x + x2 = 0 + 69 Combine like terms: -69 + 69 = 0 0 + -8x + x2 = 0 + 69 -8x + x2 = 0 + 69 Combine like terms: 0 + 69 = 69 -8x + x2 = 69 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 69 + 16 Reorder the terms: 16 + -8x + x2 = 69 + 16 Combine like terms: 69 + 16 = 85 16 + -8x + x2 = 85 Factor a perfect square on the left side: (x + -4)(x + -4) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (x + -4) equal to 9.219544457 and -9.219544457.Subproblem 1
x + -4 = 9.219544457 Simplifying x + -4 = 9.219544457 Reorder the terms: -4 + x = 9.219544457 Solving -4 + x = 9.219544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 9.219544457 + 4 Combine like terms: -4 + 4 = 0 0 + x = 9.219544457 + 4 x = 9.219544457 + 4 Combine like terms: 9.219544457 + 4 = 13.219544457 x = 13.219544457 Simplifying x = 13.219544457Subproblem 2
x + -4 = -9.219544457 Simplifying x + -4 = -9.219544457 Reorder the terms: -4 + x = -9.219544457 Solving -4 + x = -9.219544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -9.219544457 + 4 Combine like terms: -4 + 4 = 0 0 + x = -9.219544457 + 4 x = -9.219544457 + 4 Combine like terms: -9.219544457 + 4 = -5.219544457 x = -5.219544457 Simplifying x = -5.219544457Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.219544457, -5.219544457}
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