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Simplifying 20x + 20 + -8x * x + -24 = -16x * x + 190x + 24 Multiply x * x 20x + 20 + -8x2 + -24 = -16x * x + 190x + 24 Reorder the terms: 20 + -24 + 20x + -8x2 = -16x * x + 190x + 24 Combine like terms: 20 + -24 = -4 -4 + 20x + -8x2 = -16x * x + 190x + 24 Multiply x * x -4 + 20x + -8x2 = -16x2 + 190x + 24 Reorder the terms: -4 + 20x + -8x2 = 24 + 190x + -16x2 Solving -4 + 20x + -8x2 = 24 + 190x + -16x2 Solving for variable 'x'. Reorder the terms: -4 + -24 + 20x + -190x + -8x2 + 16x2 = 24 + 190x + -16x2 + -24 + -190x + 16x2 Combine like terms: -4 + -24 = -28 -28 + 20x + -190x + -8x2 + 16x2 = 24 + 190x + -16x2 + -24 + -190x + 16x2 Combine like terms: 20x + -190x = -170x -28 + -170x + -8x2 + 16x2 = 24 + 190x + -16x2 + -24 + -190x + 16x2 Combine like terms: -8x2 + 16x2 = 8x2 -28 + -170x + 8x2 = 24 + 190x + -16x2 + -24 + -190x + 16x2 Reorder the terms: -28 + -170x + 8x2 = 24 + -24 + 190x + -190x + -16x2 + 16x2 Combine like terms: 24 + -24 = 0 -28 + -170x + 8x2 = 0 + 190x + -190x + -16x2 + 16x2 -28 + -170x + 8x2 = 190x + -190x + -16x2 + 16x2 Combine like terms: 190x + -190x = 0 -28 + -170x + 8x2 = 0 + -16x2 + 16x2 -28 + -170x + 8x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -28 + -170x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + -85x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-14 + -85x + 4x2)' equal to zero and attempt to solve: Simplifying -14 + -85x + 4x2 = 0 Solving -14 + -85x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.5 + -21.25x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -21.25x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -21.25x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -21.25x + x2 = 0 + 3.5 -21.25x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -21.25x + x2 = 3.5 The x term is -21.25x. Take half its coefficient (-10.625). Square it (112.890625) and add it to both sides. Add '112.890625' to each side of the equation. -21.25x + 112.890625 + x2 = 3.5 + 112.890625 Reorder the terms: 112.890625 + -21.25x + x2 = 3.5 + 112.890625 Combine like terms: 3.5 + 112.890625 = 116.390625 112.890625 + -21.25x + x2 = 116.390625 Factor a perfect square on the left side: (x + -10.625)(x + -10.625) = 116.390625 Calculate the square root of the right side: 10.788448684 Break this problem into two subproblems by setting (x + -10.625) equal to 10.788448684 and -10.788448684.Subproblem 1
x + -10.625 = 10.788448684 Simplifying x + -10.625 = 10.788448684 Reorder the terms: -10.625 + x = 10.788448684 Solving -10.625 + x = 10.788448684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.625' to each side of the equation. -10.625 + 10.625 + x = 10.788448684 + 10.625 Combine like terms: -10.625 + 10.625 = 0.000 0.000 + x = 10.788448684 + 10.625 x = 10.788448684 + 10.625 Combine like terms: 10.788448684 + 10.625 = 21.413448684 x = 21.413448684 Simplifying x = 21.413448684Subproblem 2
x + -10.625 = -10.788448684 Simplifying x + -10.625 = -10.788448684 Reorder the terms: -10.625 + x = -10.788448684 Solving -10.625 + x = -10.788448684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.625' to each side of the equation. -10.625 + 10.625 + x = -10.788448684 + 10.625 Combine like terms: -10.625 + 10.625 = 0.000 0.000 + x = -10.788448684 + 10.625 x = -10.788448684 + 10.625 Combine like terms: -10.788448684 + 10.625 = -0.163448684 x = -0.163448684 Simplifying x = -0.163448684Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.413448684, -0.163448684}Solution
x = {21.413448684, -0.163448684}
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