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Simplifying 4x2 + 0.41x + -1.72 = 0 Reorder the terms: -1.72 + 0.41x + 4x2 = 0 Solving -1.72 + 0.41x + 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'. -0.43 + 0.1025x + x2 = 0 Move the constant term to the right: Add '0.43' to each side of the equation. -0.43 + 0.1025x + 0.43 + x2 = 0 + 0.43 Reorder the terms: -0.43 + 0.43 + 0.1025x + x2 = 0 + 0.43 Combine like terms: -0.43 + 0.43 = 0.00 0.00 + 0.1025x + x2 = 0 + 0.43 0.1025x + x2 = 0 + 0.43 Combine like terms: 0 + 0.43 = 0.43 0.1025x + x2 = 0.43 The x term is 0.1025x. Take half its coefficient (0.05125). Square it (0.0026265625) and add it to both sides. Add '0.0026265625' to each side of the equation. 0.1025x + 0.0026265625 + x2 = 0.43 + 0.0026265625 Reorder the terms: 0.0026265625 + 0.1025x + x2 = 0.43 + 0.0026265625 Combine like terms: 0.43 + 0.0026265625 = 0.4326265625 0.0026265625 + 0.1025x + x2 = 0.4326265625 Factor a perfect square on the left side: (x + 0.05125)(x + 0.05125) = 0.4326265625 Calculate the square root of the right side: 0.657743539 Break this problem into two subproblems by setting (x + 0.05125) equal to 0.657743539 and -0.657743539.Subproblem 1
x + 0.05125 = 0.657743539 Simplifying x + 0.05125 = 0.657743539 Reorder the terms: 0.05125 + x = 0.657743539 Solving 0.05125 + x = 0.657743539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05125' to each side of the equation. 0.05125 + -0.05125 + x = 0.657743539 + -0.05125 Combine like terms: 0.05125 + -0.05125 = 0.00000 0.00000 + x = 0.657743539 + -0.05125 x = 0.657743539 + -0.05125 Combine like terms: 0.657743539 + -0.05125 = 0.606493539 x = 0.606493539 Simplifying x = 0.606493539Subproblem 2
x + 0.05125 = -0.657743539 Simplifying x + 0.05125 = -0.657743539 Reorder the terms: 0.05125 + x = -0.657743539 Solving 0.05125 + x = -0.657743539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05125' to each side of the equation. 0.05125 + -0.05125 + x = -0.657743539 + -0.05125 Combine like terms: 0.05125 + -0.05125 = 0.00000 0.00000 + x = -0.657743539 + -0.05125 x = -0.657743539 + -0.05125 Combine like terms: -0.657743539 + -0.05125 = -0.708993539 x = -0.708993539 Simplifying x = -0.708993539Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.606493539, -0.708993539}
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