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Simplifying 7x2 + -20 = 6x Reorder the terms: -20 + 7x2 = 6x Solving -20 + 7x2 = 6x Solving for variable 'x'. Reorder the terms: -20 + -6x + 7x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -20 + -6x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.857142857 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + -0.8571428571x + 2.857142857 + x2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + -0.8571428571x + x2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + -0.8571428571x + x2 = 0 + 2.857142857 -0.8571428571x + x2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 -0.8571428571x + x2 = 2.857142857 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 = 2.857142857 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 2.857142857 + 0.1836734694 Combine like terms: 2.857142857 + 0.1836734694 = 3.0408163264 0.1836734694 + -0.8571428571x + x2 = 3.0408163264 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 3.0408163264 Calculate the square root of the right side: 1.743793659 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 1.743793659 and -1.743793659.Subproblem 1
x + -0.4285714286 = 1.743793659 Simplifying x + -0.4285714286 = 1.743793659 Reorder the terms: -0.4285714286 + x = 1.743793659 Solving -0.4285714286 + x = 1.743793659 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 = 1.743793659 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 1.743793659 + 0.4285714286 x = 1.743793659 + 0.4285714286 Combine like terms: 1.743793659 + 0.4285714286 = 2.1723650876 x = 2.1723650876 Simplifying x = 2.1723650876Subproblem 2
x + -0.4285714286 = -1.743793659 Simplifying x + -0.4285714286 = -1.743793659 Reorder the terms: -0.4285714286 + x = -1.743793659 Solving -0.4285714286 + x = -1.743793659 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 = -1.743793659 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -1.743793659 + 0.4285714286 x = -1.743793659 + 0.4285714286 Combine like terms: -1.743793659 + 0.4285714286 = -1.3152222304 x = -1.3152222304 Simplifying x = -1.3152222304Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1723650876, -1.3152222304}
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