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Simplifying 8(2x + 1)(x + -5) = 121 Reorder the terms: 8(1 + 2x)(x + -5) = 121 Reorder the terms: 8(1 + 2x)(-5 + x) = 121 Multiply (1 + 2x) * (-5 + x) 8(1(-5 + x) + 2x * (-5 + x)) = 121 8((-5 * 1 + x * 1) + 2x * (-5 + x)) = 121 8((-5 + 1x) + 2x * (-5 + x)) = 121 8(-5 + 1x + (-5 * 2x + x * 2x)) = 121 8(-5 + 1x + (-10x + 2x2)) = 121 Combine like terms: 1x + -10x = -9x 8(-5 + -9x + 2x2) = 121 (-5 * 8 + -9x * 8 + 2x2 * 8) = 121 (-40 + -72x + 16x2) = 121 Solving -40 + -72x + 16x2 = 121 Solving for variable 'x'. Reorder the terms: -40 + -121 + -72x + 16x2 = 121 + -121 Combine like terms: -40 + -121 = -161 -161 + -72x + 16x2 = 121 + -121 Combine like terms: 121 + -121 = 0 -161 + -72x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -10.0625 + -4.5x + x2 = 0 Move the constant term to the right: Add '10.0625' to each side of the equation. -10.0625 + -4.5x + 10.0625 + x2 = 0 + 10.0625 Reorder the terms: -10.0625 + 10.0625 + -4.5x + x2 = 0 + 10.0625 Combine like terms: -10.0625 + 10.0625 = 0.0000 0.0000 + -4.5x + x2 = 0 + 10.0625 -4.5x + x2 = 0 + 10.0625 Combine like terms: 0 + 10.0625 = 10.0625 -4.5x + x2 = 10.0625 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 10.0625 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 10.0625 + 5.0625 Combine like terms: 10.0625 + 5.0625 = 15.125 5.0625 + -4.5x + x2 = 15.125 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 15.125 Calculate the square root of the right side: 3.889087297 Break this problem into two subproblems by setting (x + -2.25) equal to 3.889087297 and -3.889087297.Subproblem 1
x + -2.25 = 3.889087297 Simplifying x + -2.25 = 3.889087297 Reorder the terms: -2.25 + x = 3.889087297 Solving -2.25 + x = 3.889087297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 3.889087297 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 3.889087297 + 2.25 x = 3.889087297 + 2.25 Combine like terms: 3.889087297 + 2.25 = 6.139087297 x = 6.139087297 Simplifying x = 6.139087297Subproblem 2
x + -2.25 = -3.889087297 Simplifying x + -2.25 = -3.889087297 Reorder the terms: -2.25 + x = -3.889087297 Solving -2.25 + x = -3.889087297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -3.889087297 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -3.889087297 + 2.25 x = -3.889087297 + 2.25 Combine like terms: -3.889087297 + 2.25 = -1.639087297 x = -1.639087297 Simplifying x = -1.639087297Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.139087297, -1.639087297}
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