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Simplifying 75X2 + 30X + -17 = 0 Reorder the terms: -17 + 30X + 75X2 = 0 Solving -17 + 30X + 75X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 75 the coefficient of the squared term: Divide each side by '75'. -0.2266666667 + 0.4X + X2 = 0 Move the constant term to the right: Add '0.2266666667' to each side of the equation. -0.2266666667 + 0.4X + 0.2266666667 + X2 = 0 + 0.2266666667 Reorder the terms: -0.2266666667 + 0.2266666667 + 0.4X + X2 = 0 + 0.2266666667 Combine like terms: -0.2266666667 + 0.2266666667 = 0.0000000000 0.0000000000 + 0.4X + X2 = 0 + 0.2266666667 0.4X + X2 = 0 + 0.2266666667 Combine like terms: 0 + 0.2266666667 = 0.2266666667 0.4X + X2 = 0.2266666667 The X term is 0.4X. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4X + 0.04 + X2 = 0.2266666667 + 0.04 Reorder the terms: 0.04 + 0.4X + X2 = 0.2266666667 + 0.04 Combine like terms: 0.2266666667 + 0.04 = 0.2666666667 0.04 + 0.4X + X2 = 0.2666666667 Factor a perfect square on the left side: (X + 0.2)(X + 0.2) = 0.2666666667 Calculate the square root of the right side: 0.51639778 Break this problem into two subproblems by setting (X + 0.2) equal to 0.51639778 and -0.51639778.Subproblem 1
X + 0.2 = 0.51639778 Simplifying X + 0.2 = 0.51639778 Reorder the terms: 0.2 + X = 0.51639778 Solving 0.2 + X = 0.51639778 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + X = 0.51639778 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + X = 0.51639778 + -0.2 X = 0.51639778 + -0.2 Combine like terms: 0.51639778 + -0.2 = 0.31639778 X = 0.31639778 Simplifying X = 0.31639778Subproblem 2
X + 0.2 = -0.51639778 Simplifying X + 0.2 = -0.51639778 Reorder the terms: 0.2 + X = -0.51639778 Solving 0.2 + X = -0.51639778 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + X = -0.51639778 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + X = -0.51639778 + -0.2 X = -0.51639778 + -0.2 Combine like terms: -0.51639778 + -0.2 = -0.71639778 X = -0.71639778 Simplifying X = -0.71639778Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.31639778, -0.71639778}
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