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Simplifying 7x2 + -13x + -28 = 0 Reorder the terms: -28 + -13x + 7x2 = 0 Solving -28 + -13x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4 + -1.857142857x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1.857142857x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -1.857142857x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1.857142857x + x2 = 0 + 4 -1.857142857x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1.857142857x + x2 = 4 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 = 4 + 0.8622448978 Reorder the terms: 0.8622448978 + -1.857142857x + x2 = 4 + 0.8622448978 Combine like terms: 4 + 0.8622448978 = 4.8622448978 0.8622448978 + -1.857142857x + x2 = 4.8622448978 Factor a perfect square on the left side: (x + -0.9285714285)(x + -0.9285714285) = 4.8622448978 Calculate the square root of the right side: 2.205049863 Break this problem into two subproblems by setting (x + -0.9285714285) equal to 2.205049863 and -2.205049863.Subproblem 1
x + -0.9285714285 = 2.205049863 Simplifying x + -0.9285714285 = 2.205049863 Reorder the terms: -0.9285714285 + x = 2.205049863 Solving -0.9285714285 + x = 2.205049863 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 = 2.205049863 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = 2.205049863 + 0.9285714285 x = 2.205049863 + 0.9285714285 Combine like terms: 2.205049863 + 0.9285714285 = 3.1336212915 x = 3.1336212915 Simplifying x = 3.1336212915Subproblem 2
x + -0.9285714285 = -2.205049863 Simplifying x + -0.9285714285 = -2.205049863 Reorder the terms: -0.9285714285 + x = -2.205049863 Solving -0.9285714285 + x = -2.205049863 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 = -2.205049863 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = -2.205049863 + 0.9285714285 x = -2.205049863 + 0.9285714285 Combine like terms: -2.205049863 + 0.9285714285 = -1.2764784345 x = -1.2764784345 Simplifying x = -1.2764784345Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1336212915, -1.2764784345}
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