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Simplifying 7x2 + 13x = 5 Reorder the terms: 13x + 7x2 = 5 Solving 13x + 7x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 13x + 7x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 13x + 7x2 = 0 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 = 0.3270282735 x = 0.3270282735 Simplifying x = 0.3270282735Subproblem 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 = -2.1841711305 x = -2.1841711305 Simplifying x = -2.1841711305Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3270282735, -2.1841711305}
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