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Simplifying 7x2 + -13x + -40 = 0 Reorder the terms: -40 + -13x + 7x2 = 0 Solving -40 + -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'. -5.714285714 + -1.857142857x + x2 = 0 Move the constant term to the right: Add '5.714285714' to each side of the equation. -5.714285714 + -1.857142857x + 5.714285714 + x2 = 0 + 5.714285714 Reorder the terms: -5.714285714 + 5.714285714 + -1.857142857x + x2 = 0 + 5.714285714 Combine like terms: -5.714285714 + 5.714285714 = 0.000000000 0.000000000 + -1.857142857x + x2 = 0 + 5.714285714 -1.857142857x + x2 = 0 + 5.714285714 Combine like terms: 0 + 5.714285714 = 5.714285714 -1.857142857x + x2 = 5.714285714 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 = 5.714285714 + 0.8622448978 Reorder the terms: 0.8622448978 + -1.857142857x + x2 = 5.714285714 + 0.8622448978 Combine like terms: 5.714285714 + 0.8622448978 = 6.5765306118 0.8622448978 + -1.857142857x + x2 = 6.5765306118 Factor a perfect square on the left side: (x + -0.9285714285)(x + -0.9285714285) = 6.5765306118 Calculate the square root of the right side: 2.564474724 Break this problem into two subproblems by setting (x + -0.9285714285) equal to 2.564474724 and -2.564474724.Subproblem 1
x + -0.9285714285 = 2.564474724 Simplifying x + -0.9285714285 = 2.564474724 Reorder the terms: -0.9285714285 + x = 2.564474724 Solving -0.9285714285 + x = 2.564474724 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 = 2.564474724 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = 2.564474724 + 0.9285714285 x = 2.564474724 + 0.9285714285 Combine like terms: 2.564474724 + 0.9285714285 = 3.4930461525 x = 3.4930461525 Simplifying x = 3.4930461525Subproblem 2
x + -0.9285714285 = -2.564474724 Simplifying x + -0.9285714285 = -2.564474724 Reorder the terms: -0.9285714285 + x = -2.564474724 Solving -0.9285714285 + x = -2.564474724 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 = -2.564474724 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = -2.564474724 + 0.9285714285 x = -2.564474724 + 0.9285714285 Combine like terms: -2.564474724 + 0.9285714285 = -1.6359032955 x = -1.6359032955 Simplifying x = -1.6359032955Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.4930461525, -1.6359032955}
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