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Simplifying 7x2 + 13x = 61 Reorder the terms: 13x + 7x2 = 61 Solving 13x + 7x2 = 61 Solving for variable 'x'. Reorder the terms: -61 + 13x + 7x2 = 61 + -61 Combine like terms: 61 + -61 = 0 -61 + 13x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -8.714285714 + 1.857142857x + x2 = 0 Move the constant term to the right: Add '8.714285714' to each side of the equation. -8.714285714 + 1.857142857x + 8.714285714 + x2 = 0 + 8.714285714 Reorder the terms: -8.714285714 + 8.714285714 + 1.857142857x + x2 = 0 + 8.714285714 Combine like terms: -8.714285714 + 8.714285714 = 0.000000000 0.000000000 + 1.857142857x + x2 = 0 + 8.714285714 1.857142857x + x2 = 0 + 8.714285714 Combine like terms: 0 + 8.714285714 = 8.714285714 1.857142857x + x2 = 8.714285714 The x term is 1.857142857x. Take half its coefficient (0.9285714285). Square it (0.8622448978) and add it to both sides. Add '0.8622448978' to each side of the equation. 1.857142857x + 0.8622448978 + x2 = 8.714285714 + 0.8622448978 Reorder the terms: 0.8622448978 + 1.857142857x + x2 = 8.714285714 + 0.8622448978 Combine like terms: 8.714285714 + 0.8622448978 = 9.5765306118 0.8622448978 + 1.857142857x + x2 = 9.5765306118 Factor a perfect square on the left side: (x + 0.9285714285)(x + 0.9285714285) = 9.5765306118 Calculate the square root of the right side: 3.094597003 Break this problem into two subproblems by setting (x + 0.9285714285) equal to 3.094597003 and -3.094597003.Subproblem 1
x + 0.9285714285 = 3.094597003 Simplifying x + 0.9285714285 = 3.094597003 Reorder the terms: 0.9285714285 + x = 3.094597003 Solving 0.9285714285 + x = 3.094597003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + x = 3.094597003 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + x = 3.094597003 + -0.9285714285 x = 3.094597003 + -0.9285714285 Combine like terms: 3.094597003 + -0.9285714285 = 2.1660255745 x = 2.1660255745 Simplifying x = 2.1660255745Subproblem 2
x + 0.9285714285 = -3.094597003 Simplifying x + 0.9285714285 = -3.094597003 Reorder the terms: 0.9285714285 + x = -3.094597003 Solving 0.9285714285 + x = -3.094597003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + x = -3.094597003 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + x = -3.094597003 + -0.9285714285 x = -3.094597003 + -0.9285714285 Combine like terms: -3.094597003 + -0.9285714285 = -4.0231684315 x = -4.0231684315 Simplifying x = -4.0231684315Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1660255745, -4.0231684315}
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