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Simplifying 5x2 + 13x = 550 Reorder the terms: 13x + 5x2 = 550 Solving 13x + 5x2 = 550 Solving for variable 'x'. Reorder the terms: -550 + 13x + 5x2 = 550 + -550 Combine like terms: 550 + -550 = 0 -550 + 13x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -110 + 2.6x + x2 = 0 Move the constant term to the right: Add '110' to each side of the equation. -110 + 2.6x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + 2.6x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 2.6x + x2 = 0 + 110 2.6x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 2.6x + x2 = 110 The x term is 2.6x. Take half its coefficient (1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. 2.6x + 1.69 + x2 = 110 + 1.69 Reorder the terms: 1.69 + 2.6x + x2 = 110 + 1.69 Combine like terms: 110 + 1.69 = 111.69 1.69 + 2.6x + x2 = 111.69 Factor a perfect square on the left side: (x + 1.3)(x + 1.3) = 111.69 Calculate the square root of the right side: 10.568348972 Break this problem into two subproblems by setting (x + 1.3) equal to 10.568348972 and -10.568348972.Subproblem 1
x + 1.3 = 10.568348972 Simplifying x + 1.3 = 10.568348972 Reorder the terms: 1.3 + x = 10.568348972 Solving 1.3 + x = 10.568348972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = 10.568348972 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = 10.568348972 + -1.3 x = 10.568348972 + -1.3 Combine like terms: 10.568348972 + -1.3 = 9.268348972 x = 9.268348972 Simplifying x = 9.268348972Subproblem 2
x + 1.3 = -10.568348972 Simplifying x + 1.3 = -10.568348972 Reorder the terms: 1.3 + x = -10.568348972 Solving 1.3 + x = -10.568348972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = -10.568348972 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = -10.568348972 + -1.3 x = -10.568348972 + -1.3 Combine like terms: -10.568348972 + -1.3 = -11.868348972 x = -11.868348972 Simplifying x = -11.868348972Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.268348972, -11.868348972}
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