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Simplifying 4X2 + 3.8X + -10.35 = 0 Reorder the terms: -10.35 + 3.8X + 4X2 = 0 Solving -10.35 + 3.8X + 4X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.5875 + 0.95X + X2 = 0 Move the constant term to the right: Add '2.5875' to each side of the equation. -2.5875 + 0.95X + 2.5875 + X2 = 0 + 2.5875 Reorder the terms: -2.5875 + 2.5875 + 0.95X + X2 = 0 + 2.5875 Combine like terms: -2.5875 + 2.5875 = 0.0000 0.0000 + 0.95X + X2 = 0 + 2.5875 0.95X + X2 = 0 + 2.5875 Combine like terms: 0 + 2.5875 = 2.5875 0.95X + X2 = 2.5875 The X term is 0.95X. Take half its coefficient (0.475). Square it (0.225625) and add it to both sides. Add '0.225625' to each side of the equation. 0.95X + 0.225625 + X2 = 2.5875 + 0.225625 Reorder the terms: 0.225625 + 0.95X + X2 = 2.5875 + 0.225625 Combine like terms: 2.5875 + 0.225625 = 2.813125 0.225625 + 0.95X + X2 = 2.813125 Factor a perfect square on the left side: (X + 0.475)(X + 0.475) = 2.813125 Calculate the square root of the right side: 1.677237312 Break this problem into two subproblems by setting (X + 0.475) equal to 1.677237312 and -1.677237312.Subproblem 1
X + 0.475 = 1.677237312 Simplifying X + 0.475 = 1.677237312 Reorder the terms: 0.475 + X = 1.677237312 Solving 0.475 + X = 1.677237312 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.475' to each side of the equation. 0.475 + -0.475 + X = 1.677237312 + -0.475 Combine like terms: 0.475 + -0.475 = 0.000 0.000 + X = 1.677237312 + -0.475 X = 1.677237312 + -0.475 Combine like terms: 1.677237312 + -0.475 = 1.202237312 X = 1.202237312 Simplifying X = 1.202237312Subproblem 2
X + 0.475 = -1.677237312 Simplifying X + 0.475 = -1.677237312 Reorder the terms: 0.475 + X = -1.677237312 Solving 0.475 + X = -1.677237312 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.475' to each side of the equation. 0.475 + -0.475 + X = -1.677237312 + -0.475 Combine like terms: 0.475 + -0.475 = 0.000 0.000 + X = -1.677237312 + -0.475 X = -1.677237312 + -0.475 Combine like terms: -1.677237312 + -0.475 = -2.152237312 X = -2.152237312 Simplifying X = -2.152237312Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.202237312, -2.152237312}
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