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Simplifying 25x2 + 56x + 21 = 0 Reorder the terms: 21 + 56x + 25x2 = 0 Solving 21 + 56x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.84 + 2.24x + x2 = 0 Move the constant term to the right: Add '-0.84' to each side of the equation. 0.84 + 2.24x + -0.84 + x2 = 0 + -0.84 Reorder the terms: 0.84 + -0.84 + 2.24x + x2 = 0 + -0.84 Combine like terms: 0.84 + -0.84 = 0.00 0.00 + 2.24x + x2 = 0 + -0.84 2.24x + x2 = 0 + -0.84 Combine like terms: 0 + -0.84 = -0.84 2.24x + x2 = -0.84 The x term is 2.24x. Take half its coefficient (1.12). Square it (1.2544) and add it to both sides. Add '1.2544' to each side of the equation. 2.24x + 1.2544 + x2 = -0.84 + 1.2544 Reorder the terms: 1.2544 + 2.24x + x2 = -0.84 + 1.2544 Combine like terms: -0.84 + 1.2544 = 0.4144 1.2544 + 2.24x + x2 = 0.4144 Factor a perfect square on the left side: (x + 1.12)(x + 1.12) = 0.4144 Calculate the square root of the right side: 0.643739078 Break this problem into two subproblems by setting (x + 1.12) equal to 0.643739078 and -0.643739078.Subproblem 1
x + 1.12 = 0.643739078 Simplifying x + 1.12 = 0.643739078 Reorder the terms: 1.12 + x = 0.643739078 Solving 1.12 + x = 0.643739078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.12' to each side of the equation. 1.12 + -1.12 + x = 0.643739078 + -1.12 Combine like terms: 1.12 + -1.12 = 0.00 0.00 + x = 0.643739078 + -1.12 x = 0.643739078 + -1.12 Combine like terms: 0.643739078 + -1.12 = -0.476260922 x = -0.476260922 Simplifying x = -0.476260922Subproblem 2
x + 1.12 = -0.643739078 Simplifying x + 1.12 = -0.643739078 Reorder the terms: 1.12 + x = -0.643739078 Solving 1.12 + x = -0.643739078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.12' to each side of the equation. 1.12 + -1.12 + x = -0.643739078 + -1.12 Combine like terms: 1.12 + -1.12 = 0.00 0.00 + x = -0.643739078 + -1.12 x = -0.643739078 + -1.12 Combine like terms: -0.643739078 + -1.12 = -1.763739078 x = -1.763739078 Simplifying x = -1.763739078Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.476260922, -1.763739078}
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