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Simplifying (x + -9)(x + 5) = 53 Reorder the terms: (-9 + x)(x + 5) = 53 Reorder the terms: (-9 + x)(5 + x) = 53 Multiply (-9 + x) * (5 + x) (-9(5 + x) + x(5 + x)) = 53 ((5 * -9 + x * -9) + x(5 + x)) = 53 ((-45 + -9x) + x(5 + x)) = 53 (-45 + -9x + (5 * x + x * x)) = 53 (-45 + -9x + (5x + x2)) = 53 Combine like terms: -9x + 5x = -4x (-45 + -4x + x2) = 53 Solving -45 + -4x + x2 = 53 Solving for variable 'x'. Reorder the terms: -45 + -53 + -4x + x2 = 53 + -53 Combine like terms: -45 + -53 = -98 -98 + -4x + x2 = 53 + -53 Combine like terms: 53 + -53 = 0 -98 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + -4x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + -4x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + -4x + x2 = 0 + 98 -4x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 -4x + x2 = 98 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 98 + 4 Reorder the terms: 4 + -4x + x2 = 98 + 4 Combine like terms: 98 + 4 = 102 4 + -4x + x2 = 102 Factor a perfect square on the left side: (x + -2)(x + -2) = 102 Calculate the square root of the right side: 10.099504938 Break this problem into two subproblems by setting (x + -2) equal to 10.099504938 and -10.099504938.Subproblem 1
x + -2 = 10.099504938 Simplifying x + -2 = 10.099504938 Reorder the terms: -2 + x = 10.099504938 Solving -2 + x = 10.099504938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 10.099504938 + 2 Combine like terms: -2 + 2 = 0 0 + x = 10.099504938 + 2 x = 10.099504938 + 2 Combine like terms: 10.099504938 + 2 = 12.099504938 x = 12.099504938 Simplifying x = 12.099504938Subproblem 2
x + -2 = -10.099504938 Simplifying x + -2 = -10.099504938 Reorder the terms: -2 + x = -10.099504938 Solving -2 + x = -10.099504938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -10.099504938 + 2 Combine like terms: -2 + 2 = 0 0 + x = -10.099504938 + 2 x = -10.099504938 + 2 Combine like terms: -10.099504938 + 2 = -8.099504938 x = -8.099504938 Simplifying x = -8.099504938Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.099504938, -8.099504938}
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