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Simplifying 0.25X2 + 0.33X + -0.75 = 0 Reorder the terms: -0.75 + 0.33X + 0.25X2 = 0 Solving -0.75 + 0.33X + 0.25X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -3 + 1.32X + X2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 1.32X + 3 + X2 = 0 + 3 Reorder the terms: -3 + 3 + 1.32X + X2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 1.32X + X2 = 0 + 3 1.32X + X2 = 0 + 3 Combine like terms: 0 + 3 = 3 1.32X + X2 = 3 The X term is 1.32X. Take half its coefficient (0.66). Square it (0.4356) and add it to both sides. Add '0.4356' to each side of the equation. 1.32X + 0.4356 + X2 = 3 + 0.4356 Reorder the terms: 0.4356 + 1.32X + X2 = 3 + 0.4356 Combine like terms: 3 + 0.4356 = 3.4356 0.4356 + 1.32X + X2 = 3.4356 Factor a perfect square on the left side: (X + 0.66)(X + 0.66) = 3.4356 Calculate the square root of the right side: 1.853537159 Break this problem into two subproblems by setting (X + 0.66) equal to 1.853537159 and -1.853537159.Subproblem 1
X + 0.66 = 1.853537159 Simplifying X + 0.66 = 1.853537159 Reorder the terms: 0.66 + X = 1.853537159 Solving 0.66 + X = 1.853537159 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.66' to each side of the equation. 0.66 + -0.66 + X = 1.853537159 + -0.66 Combine like terms: 0.66 + -0.66 = 0.00 0.00 + X = 1.853537159 + -0.66 X = 1.853537159 + -0.66 Combine like terms: 1.853537159 + -0.66 = 1.193537159 X = 1.193537159 Simplifying X = 1.193537159Subproblem 2
X + 0.66 = -1.853537159 Simplifying X + 0.66 = -1.853537159 Reorder the terms: 0.66 + X = -1.853537159 Solving 0.66 + X = -1.853537159 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.66' to each side of the equation. 0.66 + -0.66 + X = -1.853537159 + -0.66 Combine like terms: 0.66 + -0.66 = 0.00 0.00 + X = -1.853537159 + -0.66 X = -1.853537159 + -0.66 Combine like terms: -1.853537159 + -0.66 = -2.513537159 X = -2.513537159 Simplifying X = -2.513537159Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.193537159, -2.513537159}
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