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Simplifying 4x2 + 1.52x + -1.52 = 0 Reorder the terms: -1.52 + 1.52x + 4x2 = 0 Solving -1.52 + 1.52x + 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'. -0.38 + 0.38x + x2 = 0 Move the constant term to the right: Add '0.38' to each side of the equation. -0.38 + 0.38x + 0.38 + x2 = 0 + 0.38 Reorder the terms: -0.38 + 0.38 + 0.38x + x2 = 0 + 0.38 Combine like terms: -0.38 + 0.38 = 0.00 0.00 + 0.38x + x2 = 0 + 0.38 0.38x + x2 = 0 + 0.38 Combine like terms: 0 + 0.38 = 0.38 0.38x + x2 = 0.38 The x term is 0.38x. Take half its coefficient (0.19). Square it (0.0361) and add it to both sides. Add '0.0361' to each side of the equation. 0.38x + 0.0361 + x2 = 0.38 + 0.0361 Reorder the terms: 0.0361 + 0.38x + x2 = 0.38 + 0.0361 Combine like terms: 0.38 + 0.0361 = 0.4161 0.0361 + 0.38x + x2 = 0.4161 Factor a perfect square on the left side: (x + 0.19)(x + 0.19) = 0.4161 Calculate the square root of the right side: 0.645058137 Break this problem into two subproblems by setting (x + 0.19) equal to 0.645058137 and -0.645058137.Subproblem 1
x + 0.19 = 0.645058137 Simplifying x + 0.19 = 0.645058137 Reorder the terms: 0.19 + x = 0.645058137 Solving 0.19 + x = 0.645058137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.19' to each side of the equation. 0.19 + -0.19 + x = 0.645058137 + -0.19 Combine like terms: 0.19 + -0.19 = 0.00 0.00 + x = 0.645058137 + -0.19 x = 0.645058137 + -0.19 Combine like terms: 0.645058137 + -0.19 = 0.455058137 x = 0.455058137 Simplifying x = 0.455058137Subproblem 2
x + 0.19 = -0.645058137 Simplifying x + 0.19 = -0.645058137 Reorder the terms: 0.19 + x = -0.645058137 Solving 0.19 + x = -0.645058137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.19' to each side of the equation. 0.19 + -0.19 + x = -0.645058137 + -0.19 Combine like terms: 0.19 + -0.19 = 0.00 0.00 + x = -0.645058137 + -0.19 x = -0.645058137 + -0.19 Combine like terms: -0.645058137 + -0.19 = -0.835058137 x = -0.835058137 Simplifying x = -0.835058137Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.455058137, -0.835058137}
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