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Simplifying 5x2 + 36x + -5 = 0 Reorder the terms: -5 + 36x + 5x2 = 0 Solving -5 + 36x + 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'. -1 + 7.2x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 7.2x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 7.2x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 7.2x + x2 = 0 + 1 7.2x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 7.2x + x2 = 1 The x term is 7.2x. Take half its coefficient (3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. 7.2x + 12.96 + x2 = 1 + 12.96 Reorder the terms: 12.96 + 7.2x + x2 = 1 + 12.96 Combine like terms: 1 + 12.96 = 13.96 12.96 + 7.2x + x2 = 13.96 Factor a perfect square on the left side: (x + 3.6)(x + 3.6) = 13.96 Calculate the square root of the right side: 3.736308338 Break this problem into two subproblems by setting (x + 3.6) equal to 3.736308338 and -3.736308338.Subproblem 1
x + 3.6 = 3.736308338 Simplifying x + 3.6 = 3.736308338 Reorder the terms: 3.6 + x = 3.736308338 Solving 3.6 + x = 3.736308338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + x = 3.736308338 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + x = 3.736308338 + -3.6 x = 3.736308338 + -3.6 Combine like terms: 3.736308338 + -3.6 = 0.136308338 x = 0.136308338 Simplifying x = 0.136308338Subproblem 2
x + 3.6 = -3.736308338 Simplifying x + 3.6 = -3.736308338 Reorder the terms: 3.6 + x = -3.736308338 Solving 3.6 + x = -3.736308338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + x = -3.736308338 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + x = -3.736308338 + -3.6 x = -3.736308338 + -3.6 Combine like terms: -3.736308338 + -3.6 = -7.336308338 x = -7.336308338 Simplifying x = -7.336308338Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.136308338, -7.336308338}
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