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Simplifying 5x2 + 53x + -72 = 0 Reorder the terms: -72 + 53x + 5x2 = 0 Solving -72 + 53x + 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'. -14.4 + 10.6x + x2 = 0 Move the constant term to the right: Add '14.4' to each side of the equation. -14.4 + 10.6x + 14.4 + x2 = 0 + 14.4 Reorder the terms: -14.4 + 14.4 + 10.6x + x2 = 0 + 14.4 Combine like terms: -14.4 + 14.4 = 0.0 0.0 + 10.6x + x2 = 0 + 14.4 10.6x + x2 = 0 + 14.4 Combine like terms: 0 + 14.4 = 14.4 10.6x + x2 = 14.4 The x term is 10.6x. Take half its coefficient (5.3). Square it (28.09) and add it to both sides. Add '28.09' to each side of the equation. 10.6x + 28.09 + x2 = 14.4 + 28.09 Reorder the terms: 28.09 + 10.6x + x2 = 14.4 + 28.09 Combine like terms: 14.4 + 28.09 = 42.49 28.09 + 10.6x + x2 = 42.49 Factor a perfect square on the left side: (x + 5.3)(x + 5.3) = 42.49 Calculate the square root of the right side: 6.518435395 Break this problem into two subproblems by setting (x + 5.3) equal to 6.518435395 and -6.518435395.Subproblem 1
x + 5.3 = 6.518435395 Simplifying x + 5.3 = 6.518435395 Reorder the terms: 5.3 + x = 6.518435395 Solving 5.3 + x = 6.518435395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.3' to each side of the equation. 5.3 + -5.3 + x = 6.518435395 + -5.3 Combine like terms: 5.3 + -5.3 = 0.0 0.0 + x = 6.518435395 + -5.3 x = 6.518435395 + -5.3 Combine like terms: 6.518435395 + -5.3 = 1.218435395 x = 1.218435395 Simplifying x = 1.218435395Subproblem 2
x + 5.3 = -6.518435395 Simplifying x + 5.3 = -6.518435395 Reorder the terms: 5.3 + x = -6.518435395 Solving 5.3 + x = -6.518435395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.3' to each side of the equation. 5.3 + -5.3 + x = -6.518435395 + -5.3 Combine like terms: 5.3 + -5.3 = 0.0 0.0 + x = -6.518435395 + -5.3 x = -6.518435395 + -5.3 Combine like terms: -6.518435395 + -5.3 = -11.818435395 x = -11.818435395 Simplifying x = -11.818435395Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.218435395, -11.818435395}
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