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Simplifying 10x2 + 25x + 3 = 0 Reorder the terms: 3 + 25x + 10x2 = 0 Solving 3 + 25x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.3 + 2.5x + x2 = 0 Move the constant term to the right: Add '-0.3' to each side of the equation. 0.3 + 2.5x + -0.3 + x2 = 0 + -0.3 Reorder the terms: 0.3 + -0.3 + 2.5x + x2 = 0 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + 2.5x + x2 = 0 + -0.3 2.5x + x2 = 0 + -0.3 Combine like terms: 0 + -0.3 = -0.3 2.5x + x2 = -0.3 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 = -0.3 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -0.3 + 1.5625 Combine like terms: -0.3 + 1.5625 = 1.2625 1.5625 + 2.5x + x2 = 1.2625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 1.2625 Calculate the square root of the right side: 1.123610253 Break this problem into two subproblems by setting (x + 1.25) equal to 1.123610253 and -1.123610253.Subproblem 1
x + 1.25 = 1.123610253 Simplifying x + 1.25 = 1.123610253 Reorder the terms: 1.25 + x = 1.123610253 Solving 1.25 + x = 1.123610253 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 = 1.123610253 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.123610253 + -1.25 x = 1.123610253 + -1.25 Combine like terms: 1.123610253 + -1.25 = -0.126389747 x = -0.126389747 Simplifying x = -0.126389747Subproblem 2
x + 1.25 = -1.123610253 Simplifying x + 1.25 = -1.123610253 Reorder the terms: 1.25 + x = -1.123610253 Solving 1.25 + x = -1.123610253 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 = -1.123610253 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.123610253 + -1.25 x = -1.123610253 + -1.25 Combine like terms: -1.123610253 + -1.25 = -2.373610253 x = -2.373610253 Simplifying x = -2.373610253Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.126389747, -2.373610253}
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