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Simplifying 5X + -8X + 3 = 8X(-3X + 5) Reorder the terms: 3 + 5X + -8X = 8X(-3X + 5) Combine like terms: 5X + -8X = -3X 3 + -3X = 8X(-3X + 5) Reorder the terms: 3 + -3X = 8X(5 + -3X) 3 + -3X = (5 * 8X + -3X * 8X) 3 + -3X = (40X + -24X2) Solving 3 + -3X = 40X + -24X2 Solving for variable 'X'. Combine like terms: -3X + -40X = -43X 3 + -43X + 24X2 = 40X + -24X2 + -40X + 24X2 Reorder the terms: 3 + -43X + 24X2 = 40X + -40X + -24X2 + 24X2 Combine like terms: 40X + -40X = 0 3 + -43X + 24X2 = 0 + -24X2 + 24X2 3 + -43X + 24X2 = -24X2 + 24X2 Combine like terms: -24X2 + 24X2 = 0 3 + -43X + 24X2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. 0.125 + -1.791666667X + X2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -1.791666667X + -0.125 + X2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -1.791666667X + X2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -1.791666667X + X2 = 0 + -0.125 -1.791666667X + X2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -1.791666667X + X2 = -0.125 The X term is -1.791666667X. Take half its coefficient (-0.8958333335). Square it (0.8025173614) and add it to both sides. Add '0.8025173614' to each side of the equation. -1.791666667X + 0.8025173614 + X2 = -0.125 + 0.8025173614 Reorder the terms: 0.8025173614 + -1.791666667X + X2 = -0.125 + 0.8025173614 Combine like terms: -0.125 + 0.8025173614 = 0.6775173614 0.8025173614 + -1.791666667X + X2 = 0.6775173614 Factor a perfect square on the left side: (X + -0.8958333335)(X + -0.8958333335) = 0.6775173614 Calculate the square root of the right side: 0.823114428 Break this problem into two subproblems by setting (X + -0.8958333335) equal to 0.823114428 and -0.823114428.Subproblem 1
X + -0.8958333335 = 0.823114428 Simplifying X + -0.8958333335 = 0.823114428 Reorder the terms: -0.8958333335 + X = 0.823114428 Solving -0.8958333335 + X = 0.823114428 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.8958333335' to each side of the equation. -0.8958333335 + 0.8958333335 + X = 0.823114428 + 0.8958333335 Combine like terms: -0.8958333335 + 0.8958333335 = 0.0000000000 0.0000000000 + X = 0.823114428 + 0.8958333335 X = 0.823114428 + 0.8958333335 Combine like terms: 0.823114428 + 0.8958333335 = 1.7189477615 X = 1.7189477615 Simplifying X = 1.7189477615Subproblem 2
X + -0.8958333335 = -0.823114428 Simplifying X + -0.8958333335 = -0.823114428 Reorder the terms: -0.8958333335 + X = -0.823114428 Solving -0.8958333335 + X = -0.823114428 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.8958333335' to each side of the equation. -0.8958333335 + 0.8958333335 + X = -0.823114428 + 0.8958333335 Combine like terms: -0.8958333335 + 0.8958333335 = 0.0000000000 0.0000000000 + X = -0.823114428 + 0.8958333335 X = -0.823114428 + 0.8958333335 Combine like terms: -0.823114428 + 0.8958333335 = 0.0727189055 X = 0.0727189055 Simplifying X = 0.0727189055Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.7189477615, 0.0727189055}
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