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Simplifying 4x2 + 21x + 25 = 0 Reorder the terms: 25 + 21x + 4x2 = 0 Solving 25 + 21x + 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'. 6.25 + 5.25x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + 5.25x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + 5.25x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + 5.25x + x2 = 0 + -6.25 5.25x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 5.25x + x2 = -6.25 The x term is 5.25x. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25x + 6.890625 + x2 = -6.25 + 6.890625 Reorder the terms: 6.890625 + 5.25x + x2 = -6.25 + 6.890625 Combine like terms: -6.25 + 6.890625 = 0.640625 6.890625 + 5.25x + x2 = 0.640625 Factor a perfect square on the left side: (x + 2.625)(x + 2.625) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (x + 2.625) equal to 0.80039053 and -0.80039053.Subproblem 1
x + 2.625 = 0.80039053 Simplifying x + 2.625 = 0.80039053 Reorder the terms: 2.625 + x = 0.80039053 Solving 2.625 + x = 0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = 0.80039053 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 0.80039053 + -2.625 x = 0.80039053 + -2.625 Combine like terms: 0.80039053 + -2.625 = -1.82460947 x = -1.82460947 Simplifying x = -1.82460947Subproblem 2
x + 2.625 = -0.80039053 Simplifying x + 2.625 = -0.80039053 Reorder the terms: 2.625 + x = -0.80039053 Solving 2.625 + x = -0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = -0.80039053 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -0.80039053 + -2.625 x = -0.80039053 + -2.625 Combine like terms: -0.80039053 + -2.625 = -3.42539053 x = -3.42539053 Simplifying x = -3.42539053Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.82460947, -3.42539053}
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