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Simplifying (2x2 + -7x + 3) + -1(9x2 + -1x) = 0 Reorder the terms: (3 + -7x + 2x2) + -1(9x2 + -1x) = 0 Remove parenthesis around (3 + -7x + 2x2) 3 + -7x + 2x2 + -1(9x2 + -1x) = 0 Reorder the terms: 3 + -7x + 2x2 + -1(-1x + 9x2) = 0 3 + -7x + 2x2 + (-1x * -1 + 9x2 * -1) = 0 3 + -7x + 2x2 + (1x + -9x2) = 0 Reorder the terms: 3 + -7x + 1x + 2x2 + -9x2 = 0 Combine like terms: -7x + 1x = -6x 3 + -6x + 2x2 + -9x2 = 0 Combine like terms: 2x2 + -9x2 = -7x2 3 + -6x + -7x2 = 0 Solving 3 + -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'. -0.4285714286 + 0.8571428571x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.8571428571x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 0.8571428571x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 0.8571428571x + x2 = 0 + 0.4285714286 0.8571428571x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 0.8571428571x + x2 = 0.4285714286 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 = 0.4285714286 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571x + x2 = 0.4285714286 + 0.1836734694 Combine like terms: 0.4285714286 + 0.1836734694 = 0.612244898 0.1836734694 + 0.8571428571x + x2 = 0.612244898 Factor a perfect square on the left side: (x + 0.4285714286)(x + 0.4285714286) = 0.612244898 Calculate the square root of the right side: 0.782460796 Break this problem into two subproblems by setting (x + 0.4285714286) equal to 0.782460796 and -0.782460796.Subproblem 1
x + 0.4285714286 = 0.782460796 Simplifying x + 0.4285714286 = 0.782460796 Reorder the terms: 0.4285714286 + x = 0.782460796 Solving 0.4285714286 + x = 0.782460796 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 = 0.782460796 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = 0.782460796 + -0.4285714286 x = 0.782460796 + -0.4285714286 Combine like terms: 0.782460796 + -0.4285714286 = 0.3538893674 x = 0.3538893674 Simplifying x = 0.3538893674Subproblem 2
x + 0.4285714286 = -0.782460796 Simplifying x + 0.4285714286 = -0.782460796 Reorder the terms: 0.4285714286 + x = -0.782460796 Solving 0.4285714286 + x = -0.782460796 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 = -0.782460796 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = -0.782460796 + -0.4285714286 x = -0.782460796 + -0.4285714286 Combine like terms: -0.782460796 + -0.4285714286 = -1.2110322246 x = -1.2110322246 Simplifying x = -1.2110322246Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3538893674, -1.2110322246}
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