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Simplifying 5x * x + 2x + -45 = 0 Multiply x * x 5x2 + 2x + -45 = 0 Reorder the terms: -45 + 2x + 5x2 = 0 Solving -45 + 2x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9 + 0.4x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 0.4x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 0.4x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 0.4x + x2 = 0 + 9 0.4x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 0.4x + x2 = 9 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 9 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 9 + 0.04 Combine like terms: 9 + 0.04 = 9.04 0.04 + 0.4x + x2 = 9.04 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 9.04 Calculate the square root of the right side: 3.006659276 Break this problem into two subproblems by setting (x + 0.2) equal to 3.006659276 and -3.006659276.Subproblem 1
x + 0.2 = 3.006659276 Simplifying x + 0.2 = 3.006659276 Reorder the terms: 0.2 + x = 3.006659276 Solving 0.2 + x = 3.006659276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 3.006659276 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 3.006659276 + -0.2 x = 3.006659276 + -0.2 Combine like terms: 3.006659276 + -0.2 = 2.806659276 x = 2.806659276 Simplifying x = 2.806659276Subproblem 2
x + 0.2 = -3.006659276 Simplifying x + 0.2 = -3.006659276 Reorder the terms: 0.2 + x = -3.006659276 Solving 0.2 + x = -3.006659276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -3.006659276 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -3.006659276 + -0.2 x = -3.006659276 + -0.2 Combine like terms: -3.006659276 + -0.2 = -3.206659276 x = -3.206659276 Simplifying x = -3.206659276Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.806659276, -3.206659276}
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