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Simplifying 5x2 + 10x = 13 Reorder the terms: 10x + 5x2 = 13 Solving 10x + 5x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + 10x + 5x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.6 + 2x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + 2x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + 2x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + 2x + x2 = 0 + 2.6 2x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 2x + x2 = 2.6 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 2.6 + 1 Reorder the terms: 1 + 2x + x2 = 2.6 + 1 Combine like terms: 2.6 + 1 = 3.6 1 + 2x + x2 = 3.6 Factor a perfect square on the left side: (x + 1)(x + 1) = 3.6 Calculate the square root of the right side: 1.897366596 Break this problem into two subproblems by setting (x + 1) equal to 1.897366596 and -1.897366596.Subproblem 1
x + 1 = 1.897366596 Simplifying x + 1 = 1.897366596 Reorder the terms: 1 + x = 1.897366596 Solving 1 + x = 1.897366596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.897366596 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.897366596 + -1 x = 1.897366596 + -1 Combine like terms: 1.897366596 + -1 = 0.897366596 x = 0.897366596 Simplifying x = 0.897366596Subproblem 2
x + 1 = -1.897366596 Simplifying x + 1 = -1.897366596 Reorder the terms: 1 + x = -1.897366596 Solving 1 + x = -1.897366596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.897366596 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.897366596 + -1 x = -1.897366596 + -1 Combine like terms: -1.897366596 + -1 = -2.897366596 x = -2.897366596 Simplifying x = -2.897366596Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.897366596, -2.897366596}
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