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Simplifying 4x2 + 25x + -2 = 0 Reorder the terms: -2 + 25x + 4x2 = 0 Solving -2 + 25x + 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'. -0.5 + 6.25x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 6.25x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 6.25x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 6.25x + x2 = 0 + 0.5 6.25x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 6.25x + x2 = 0.5 The x term is 6.25x. Take half its coefficient (3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. 6.25x + 9.765625 + x2 = 0.5 + 9.765625 Reorder the terms: 9.765625 + 6.25x + x2 = 0.5 + 9.765625 Combine like terms: 0.5 + 9.765625 = 10.265625 9.765625 + 6.25x + x2 = 10.265625 Factor a perfect square on the left side: (x + 3.125)(x + 3.125) = 10.265625 Calculate the square root of the right side: 3.204001404 Break this problem into two subproblems by setting (x + 3.125) equal to 3.204001404 and -3.204001404.Subproblem 1
x + 3.125 = 3.204001404 Simplifying x + 3.125 = 3.204001404 Reorder the terms: 3.125 + x = 3.204001404 Solving 3.125 + x = 3.204001404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + x = 3.204001404 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + x = 3.204001404 + -3.125 x = 3.204001404 + -3.125 Combine like terms: 3.204001404 + -3.125 = 0.079001404 x = 0.079001404 Simplifying x = 0.079001404Subproblem 2
x + 3.125 = -3.204001404 Simplifying x + 3.125 = -3.204001404 Reorder the terms: 3.125 + x = -3.204001404 Solving 3.125 + x = -3.204001404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + x = -3.204001404 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + x = -3.204001404 + -3.125 x = -3.204001404 + -3.125 Combine like terms: -3.204001404 + -3.125 = -6.329001404 x = -6.329001404 Simplifying x = -6.329001404Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.079001404, -6.329001404}
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