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Simplifying 4x2 + 2x + -2 = 3 Reorder the terms: -2 + 2x + 4x2 = 3 Solving -2 + 2x + 4x2 = 3 Solving for variable 'x'. Reorder the terms: -2 + -3 + 2x + 4x2 = 3 + -3 Combine like terms: -2 + -3 = -5 -5 + 2x + 4x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -5 + 2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 0.5x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 0.5x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 0.5x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 0.5x + x2 = 0 + 1.25 0.5x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 0.5x + x2 = 1.25 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 1.25 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 1.25 + 0.0625 Combine like terms: 1.25 + 0.0625 = 1.3125 0.0625 + 0.5x + x2 = 1.3125 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 1.3125 Calculate the square root of the right side: 1.145643924 Break this problem into two subproblems by setting (x + 0.25) equal to 1.145643924 and -1.145643924.Subproblem 1
x + 0.25 = 1.145643924 Simplifying x + 0.25 = 1.145643924 Reorder the terms: 0.25 + x = 1.145643924 Solving 0.25 + x = 1.145643924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.145643924 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.145643924 + -0.25 x = 1.145643924 + -0.25 Combine like terms: 1.145643924 + -0.25 = 0.895643924 x = 0.895643924 Simplifying x = 0.895643924Subproblem 2
x + 0.25 = -1.145643924 Simplifying x + 0.25 = -1.145643924 Reorder the terms: 0.25 + x = -1.145643924 Solving 0.25 + x = -1.145643924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.145643924 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.145643924 + -0.25 x = -1.145643924 + -0.25 Combine like terms: -1.145643924 + -0.25 = -1.395643924 x = -1.395643924 Simplifying x = -1.395643924Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.895643924, -1.395643924}
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