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Simplifying 7x2 = 6x + 21 Reorder the terms: 7x2 = 21 + 6x Solving 7x2 = 21 + 6x Solving for variable 'x'. Reorder the terms: -21 + -6x + 7x2 = 21 + 6x + -21 + -6x Reorder the terms: -21 + -6x + 7x2 = 21 + -21 + 6x + -6x Combine like terms: 21 + -21 = 0 -21 + -6x + 7x2 = 0 + 6x + -6x -21 + -6x + 7x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -21 + -6x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -0.8571428571x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -0.8571428571x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -0.8571428571x + x2 = 0 + 3 -0.8571428571x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -0.8571428571x + x2 = 3 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 = 3 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 3 + 0.1836734694 Combine like terms: 3 + 0.1836734694 = 3.1836734694 0.1836734694 + -0.8571428571x + x2 = 3.1836734694 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 3.1836734694 Calculate the square root of the right side: 1.784285142 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 1.784285142 and -1.784285142.Subproblem 1
x + -0.4285714286 = 1.784285142 Simplifying x + -0.4285714286 = 1.784285142 Reorder the terms: -0.4285714286 + x = 1.784285142 Solving -0.4285714286 + x = 1.784285142 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 = 1.784285142 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 1.784285142 + 0.4285714286 x = 1.784285142 + 0.4285714286 Combine like terms: 1.784285142 + 0.4285714286 = 2.2128565706 x = 2.2128565706 Simplifying x = 2.2128565706Subproblem 2
x + -0.4285714286 = -1.784285142 Simplifying x + -0.4285714286 = -1.784285142 Reorder the terms: -0.4285714286 + x = -1.784285142 Solving -0.4285714286 + x = -1.784285142 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 = -1.784285142 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -1.784285142 + 0.4285714286 x = -1.784285142 + 0.4285714286 Combine like terms: -1.784285142 + 0.4285714286 = -1.3557137134 x = -1.3557137134 Simplifying x = -1.3557137134Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2128565706, -1.3557137134}
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