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Simplifying (5x2 + -7x + -2) + (9x2 + 8x + -4) = 0 Reorder the terms: (-2 + -7x + 5x2) + (9x2 + 8x + -4) = 0 Remove parenthesis around (-2 + -7x + 5x2) -2 + -7x + 5x2 + (9x2 + 8x + -4) = 0 Reorder the terms: -2 + -7x + 5x2 + (-4 + 8x + 9x2) = 0 Remove parenthesis around (-4 + 8x + 9x2) -2 + -7x + 5x2 + -4 + 8x + 9x2 = 0 Reorder the terms: -2 + -4 + -7x + 8x + 5x2 + 9x2 = 0 Combine like terms: -2 + -4 = -6 -6 + -7x + 8x + 5x2 + 9x2 = 0 Combine like terms: -7x + 8x = 1x -6 + 1x + 5x2 + 9x2 = 0 Combine like terms: 5x2 + 9x2 = 14x2 -6 + 1x + 14x2 = 0 Solving -6 + 1x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.4285714286 + 0.07142857143x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.07142857143x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 0.07142857143x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 0.07142857143x + x2 = 0 + 0.4285714286 0.07142857143x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 0.07142857143x + x2 = 0.4285714286 The x term is 0.07142857143x. Take half its coefficient (0.03571428572). Square it (0.001275510204) and add it to both sides. Add '0.001275510204' to each side of the equation. 0.07142857143x + 0.001275510204 + x2 = 0.4285714286 + 0.001275510204 Reorder the terms: 0.001275510204 + 0.07142857143x + x2 = 0.4285714286 + 0.001275510204 Combine like terms: 0.4285714286 + 0.001275510204 = 0.429846938804 0.001275510204 + 0.07142857143x + x2 = 0.429846938804 Factor a perfect square on the left side: (x + 0.03571428572)(x + 0.03571428572) = 0.429846938804 Calculate the square root of the right side: 0.655627134 Break this problem into two subproblems by setting (x + 0.03571428572) equal to 0.655627134 and -0.655627134.Subproblem 1
x + 0.03571428572 = 0.655627134 Simplifying x + 0.03571428572 = 0.655627134 Reorder the terms: 0.03571428572 + x = 0.655627134 Solving 0.03571428572 + x = 0.655627134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03571428572' to each side of the equation. 0.03571428572 + -0.03571428572 + x = 0.655627134 + -0.03571428572 Combine like terms: 0.03571428572 + -0.03571428572 = 0.00000000000 0.00000000000 + x = 0.655627134 + -0.03571428572 x = 0.655627134 + -0.03571428572 Combine like terms: 0.655627134 + -0.03571428572 = 0.61991284828 x = 0.61991284828 Simplifying x = 0.61991284828Subproblem 2
x + 0.03571428572 = -0.655627134 Simplifying x + 0.03571428572 = -0.655627134 Reorder the terms: 0.03571428572 + x = -0.655627134 Solving 0.03571428572 + x = -0.655627134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03571428572' to each side of the equation. 0.03571428572 + -0.03571428572 + x = -0.655627134 + -0.03571428572 Combine like terms: 0.03571428572 + -0.03571428572 = 0.00000000000 0.00000000000 + x = -0.655627134 + -0.03571428572 x = -0.655627134 + -0.03571428572 Combine like terms: -0.655627134 + -0.03571428572 = -0.69134141972 x = -0.69134141972 Simplifying x = -0.69134141972Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.61991284828, -0.69134141972}
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