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Simplifying 4x2 + 10x + 1 = 0 Reorder the terms: 1 + 10x + 4x2 = 0 Solving 1 + 10x + 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'. 0.25 + 2.5x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 2.5x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 2.5x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 2.5x + x2 = 0 + -0.25 2.5x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 2.5x + x2 = -0.25 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = -0.25 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -0.25 + 1.5625 Combine like terms: -0.25 + 1.5625 = 1.3125 1.5625 + 2.5x + x2 = 1.3125 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 1.3125 Calculate the square root of the right side: 1.145643924 Break this problem into two subproblems by setting (x + 1.25) equal to 1.145643924 and -1.145643924.Subproblem 1
x + 1.25 = 1.145643924 Simplifying x + 1.25 = 1.145643924 Reorder the terms: 1.25 + x = 1.145643924 Solving 1.25 + x = 1.145643924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.145643924 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.145643924 + -1.25 x = 1.145643924 + -1.25 Combine like terms: 1.145643924 + -1.25 = -0.104356076 x = -0.104356076 Simplifying x = -0.104356076Subproblem 2
x + 1.25 = -1.145643924 Simplifying x + 1.25 = -1.145643924 Reorder the terms: 1.25 + x = -1.145643924 Solving 1.25 + x = -1.145643924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.145643924 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.145643924 + -1.25 x = -1.145643924 + -1.25 Combine like terms: -1.145643924 + -1.25 = -2.395643924 x = -2.395643924 Simplifying x = -2.395643924Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.104356076, -2.395643924}
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