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Simplifying 7x2 + 6x + -15 = 0 Reorder the terms: -15 + 6x + 7x2 = 0 Solving -15 + 6x + 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'. -2.142857143 + 0.8571428571x + x2 = 0 Move the constant term to the right: Add '2.142857143' to each side of the equation. -2.142857143 + 0.8571428571x + 2.142857143 + x2 = 0 + 2.142857143 Reorder the terms: -2.142857143 + 2.142857143 + 0.8571428571x + x2 = 0 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + 0.8571428571x + x2 = 0 + 2.142857143 0.8571428571x + x2 = 0 + 2.142857143 Combine like terms: 0 + 2.142857143 = 2.142857143 0.8571428571x + x2 = 2.142857143 The x term is 0.8571428571x. Take half its coefficient (0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. 0.8571428571x + 0.1836734694 + x2 = 2.142857143 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571x + x2 = 2.142857143 + 0.1836734694 Combine like terms: 2.142857143 + 0.1836734694 = 2.3265306124 0.1836734694 + 0.8571428571x + x2 = 2.3265306124 Factor a perfect square on the left side: (x + 0.4285714286)(x + 0.4285714286) = 2.3265306124 Calculate the square root of the right side: 1.525296893 Break this problem into two subproblems by setting (x + 0.4285714286) equal to 1.525296893 and -1.525296893.Subproblem 1
x + 0.4285714286 = 1.525296893 Simplifying x + 0.4285714286 = 1.525296893 Reorder the terms: 0.4285714286 + x = 1.525296893 Solving 0.4285714286 + x = 1.525296893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = 1.525296893 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = 1.525296893 + -0.4285714286 x = 1.525296893 + -0.4285714286 Combine like terms: 1.525296893 + -0.4285714286 = 1.0967254644 x = 1.0967254644 Simplifying x = 1.0967254644Subproblem 2
x + 0.4285714286 = -1.525296893 Simplifying x + 0.4285714286 = -1.525296893 Reorder the terms: 0.4285714286 + x = -1.525296893 Solving 0.4285714286 + x = -1.525296893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = -1.525296893 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = -1.525296893 + -0.4285714286 x = -1.525296893 + -0.4285714286 Combine like terms: -1.525296893 + -0.4285714286 = -1.9538683216 x = -1.9538683216 Simplifying x = -1.9538683216Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0967254644, -1.9538683216}
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