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Simplifying 7x2 + -13x + -5 = 0 Reorder the terms: -5 + -13x + 7x2 = 0 Solving -5 + -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'. -0.7142857143 + -1.857142857x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -1.857142857x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -1.857142857x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -1.857142857x + x2 = 0 + 0.7142857143 -1.857142857x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -1.857142857x + x2 = 0.7142857143 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 = 0.7142857143 + 0.8622448978 Reorder the terms: 0.8622448978 + -1.857142857x + x2 = 0.7142857143 + 0.8622448978 Combine like terms: 0.7142857143 + 0.8622448978 = 1.5765306121 0.8622448978 + -1.857142857x + x2 = 1.5765306121 Factor a perfect square on the left side: (x + -0.9285714285)(x + -0.9285714285) = 1.5765306121 Calculate the square root of the right side: 1.255599702 Break this problem into two subproblems by setting (x + -0.9285714285) equal to 1.255599702 and -1.255599702.Subproblem 1
x + -0.9285714285 = 1.255599702 Simplifying x + -0.9285714285 = 1.255599702 Reorder the terms: -0.9285714285 + x = 1.255599702 Solving -0.9285714285 + x = 1.255599702 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 = 1.255599702 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = 1.255599702 + 0.9285714285 x = 1.255599702 + 0.9285714285 Combine like terms: 1.255599702 + 0.9285714285 = 2.1841711305 x = 2.1841711305 Simplifying x = 2.1841711305Subproblem 2
x + -0.9285714285 = -1.255599702 Simplifying x + -0.9285714285 = -1.255599702 Reorder the terms: -0.9285714285 + x = -1.255599702 Solving -0.9285714285 + x = -1.255599702 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 = -1.255599702 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = -1.255599702 + 0.9285714285 x = -1.255599702 + 0.9285714285 Combine like terms: -1.255599702 + 0.9285714285 = -0.3270282735 x = -0.3270282735 Simplifying x = -0.3270282735Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1841711305, -0.3270282735}
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