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Simplifying 7x2 + 13x + -3 = 0 Reorder the terms: -3 + 13x + 7x2 = 0 Solving -3 + 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'. -0.4285714286 + 1.857142857x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 1.857142857x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 1.857142857x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 1.857142857x + x2 = 0 + 0.4285714286 1.857142857x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 1.857142857x + x2 = 0.4285714286 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 = 0.4285714286 + 0.8622448978 Reorder the terms: 0.8622448978 + 1.857142857x + x2 = 0.4285714286 + 0.8622448978 Combine like terms: 0.4285714286 + 0.8622448978 = 1.2908163264 0.8622448978 + 1.857142857x + x2 = 1.2908163264 Factor a perfect square on the left side: (x + 0.9285714285)(x + 0.9285714285) = 1.2908163264 Calculate the square root of the right side: 1.13614098 Break this problem into two subproblems by setting (x + 0.9285714285) equal to 1.13614098 and -1.13614098.Subproblem 1
x + 0.9285714285 = 1.13614098 Simplifying x + 0.9285714285 = 1.13614098 Reorder the terms: 0.9285714285 + x = 1.13614098 Solving 0.9285714285 + x = 1.13614098 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 = 1.13614098 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + x = 1.13614098 + -0.9285714285 x = 1.13614098 + -0.9285714285 Combine like terms: 1.13614098 + -0.9285714285 = 0.2075695515 x = 0.2075695515 Simplifying x = 0.2075695515Subproblem 2
x + 0.9285714285 = -1.13614098 Simplifying x + 0.9285714285 = -1.13614098 Reorder the terms: 0.9285714285 + x = -1.13614098 Solving 0.9285714285 + x = -1.13614098 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 = -1.13614098 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + x = -1.13614098 + -0.9285714285 x = -1.13614098 + -0.9285714285 Combine like terms: -1.13614098 + -0.9285714285 = -2.0647124085 x = -2.0647124085 Simplifying x = -2.0647124085Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2075695515, -2.0647124085}
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