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Simplifying 4x2 + 0.41x + -1(0.41 * 14) = 0 Multiply 0.41 * 14 4x2 + 0.41x + -1(5.74) = 0 Multiply -1 * 5.74 4x2 + 0.41x + -5.74 = 0 Reorder the terms: -5.74 + 0.41x + 4x2 = 0 Solving -5.74 + 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'. -1.435 + 0.1025x + x2 = 0 Move the constant term to the right: Add '1.435' to each side of the equation. -1.435 + 0.1025x + 1.435 + x2 = 0 + 1.435 Reorder the terms: -1.435 + 1.435 + 0.1025x + x2 = 0 + 1.435 Combine like terms: -1.435 + 1.435 = 0.000 0.000 + 0.1025x + x2 = 0 + 1.435 0.1025x + x2 = 0 + 1.435 Combine like terms: 0 + 1.435 = 1.435 0.1025x + x2 = 1.435 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 = 1.435 + 0.0026265625 Reorder the terms: 0.0026265625 + 0.1025x + x2 = 1.435 + 0.0026265625 Combine like terms: 1.435 + 0.0026265625 = 1.4376265625 0.0026265625 + 0.1025x + x2 = 1.4376265625 Factor a perfect square on the left side: (x + 0.05125)(x + 0.05125) = 1.4376265625 Calculate the square root of the right side: 1.19901066 Break this problem into two subproblems by setting (x + 0.05125) equal to 1.19901066 and -1.19901066.Subproblem 1
x + 0.05125 = 1.19901066 Simplifying x + 0.05125 = 1.19901066 Reorder the terms: 0.05125 + x = 1.19901066 Solving 0.05125 + x = 1.19901066 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 = 1.19901066 + -0.05125 Combine like terms: 0.05125 + -0.05125 = 0.00000 0.00000 + x = 1.19901066 + -0.05125 x = 1.19901066 + -0.05125 Combine like terms: 1.19901066 + -0.05125 = 1.14776066 x = 1.14776066 Simplifying x = 1.14776066Subproblem 2
x + 0.05125 = -1.19901066 Simplifying x + 0.05125 = -1.19901066 Reorder the terms: 0.05125 + x = -1.19901066 Solving 0.05125 + x = -1.19901066 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 = -1.19901066 + -0.05125 Combine like terms: 0.05125 + -0.05125 = 0.00000 0.00000 + x = -1.19901066 + -0.05125 x = -1.19901066 + -0.05125 Combine like terms: -1.19901066 + -0.05125 = -1.25026066 x = -1.25026066 Simplifying x = -1.25026066Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.14776066, -1.25026066}
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