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Simplifying 7x2 + -6x = 5 Reorder the terms: -6x + 7x2 = 5 Solving -6x + 7x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + -6x + 7x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -6x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -0.8571428571x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -0.8571428571x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -0.8571428571x + x2 = 0 + 0.7142857143 -0.8571428571x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -0.8571428571x + x2 = 0.7142857143 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 = 0.7142857143 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 0.7142857143 + 0.1836734694 Combine like terms: 0.7142857143 + 0.1836734694 = 0.8979591837 0.1836734694 + -0.8571428571x + x2 = 0.8979591837 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 0.8979591837 Calculate the square root of the right side: 0.947607083 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 0.947607083 and -0.947607083.Subproblem 1
x + -0.4285714286 = 0.947607083 Simplifying x + -0.4285714286 = 0.947607083 Reorder the terms: -0.4285714286 + x = 0.947607083 Solving -0.4285714286 + x = 0.947607083 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 = 0.947607083 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 0.947607083 + 0.4285714286 x = 0.947607083 + 0.4285714286 Combine like terms: 0.947607083 + 0.4285714286 = 1.3761785116 x = 1.3761785116 Simplifying x = 1.3761785116Subproblem 2
x + -0.4285714286 = -0.947607083 Simplifying x + -0.4285714286 = -0.947607083 Reorder the terms: -0.4285714286 + x = -0.947607083 Solving -0.4285714286 + x = -0.947607083 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 = -0.947607083 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -0.947607083 + 0.4285714286 x = -0.947607083 + 0.4285714286 Combine like terms: -0.947607083 + 0.4285714286 = -0.5190356544 x = -0.5190356544 Simplifying x = -0.5190356544Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3761785116, -0.5190356544}
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