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Simplifying 4X2 + 6X = 3 Reorder the terms: 6X + 4X2 = 3 Solving 6X + 4X2 = 3 Solving for variable 'X'. Reorder the terms: -3 + 6X + 4X2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 6X + 4X2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 1.5X + X2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 1.5X + 0.75 + X2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 1.5X + X2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 1.5X + X2 = 0 + 0.75 1.5X + X2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 1.5X + X2 = 0.75 The X term is 1.5X. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5X + 0.5625 + X2 = 0.75 + 0.5625 Reorder the terms: 0.5625 + 1.5X + X2 = 0.75 + 0.5625 Combine like terms: 0.75 + 0.5625 = 1.3125 0.5625 + 1.5X + X2 = 1.3125 Factor a perfect square on the left side: (X + 0.75)(X + 0.75) = 1.3125 Calculate the square root of the right side: 1.145643924 Break this problem into two subproblems by setting (X + 0.75) equal to 1.145643924 and -1.145643924.Subproblem 1
X + 0.75 = 1.145643924 Simplifying X + 0.75 = 1.145643924 Reorder the terms: 0.75 + X = 1.145643924 Solving 0.75 + X = 1.145643924 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + X = 1.145643924 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + X = 1.145643924 + -0.75 X = 1.145643924 + -0.75 Combine like terms: 1.145643924 + -0.75 = 0.395643924 X = 0.395643924 Simplifying X = 0.395643924Subproblem 2
X + 0.75 = -1.145643924 Simplifying X + 0.75 = -1.145643924 Reorder the terms: 0.75 + X = -1.145643924 Solving 0.75 + X = -1.145643924 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + X = -1.145643924 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + X = -1.145643924 + -0.75 X = -1.145643924 + -0.75 Combine like terms: -1.145643924 + -0.75 = -1.895643924 X = -1.895643924 Simplifying X = -1.895643924Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.395643924, -1.895643924}
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