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Simplifying 6x = -7x2 + 9x + 3 Reorder the terms: 6x = 3 + 9x + -7x2 Solving 6x = 3 + 9x + -7x2 Solving for variable 'x'. Reorder the terms: -3 + 6x + -9x + 7x2 = 3 + 9x + -7x2 + -3 + -9x + 7x2 Combine like terms: 6x + -9x = -3x -3 + -3x + 7x2 = 3 + 9x + -7x2 + -3 + -9x + 7x2 Reorder the terms: -3 + -3x + 7x2 = 3 + -3 + 9x + -9x + -7x2 + 7x2 Combine like terms: 3 + -3 = 0 -3 + -3x + 7x2 = 0 + 9x + -9x + -7x2 + 7x2 -3 + -3x + 7x2 = 9x + -9x + -7x2 + 7x2 Combine like terms: 9x + -9x = 0 -3 + -3x + 7x2 = 0 + -7x2 + 7x2 -3 + -3x + 7x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 -3 + -3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -0.4285714286x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -0.4285714286x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -0.4285714286x + x2 = 0 + 0.4285714286 -0.4285714286x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -0.4285714286x + x2 = 0.4285714286 The x term is -0.4285714286x. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286x + 0.04591836735 + x2 = 0.4285714286 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = 0.4285714286 + 0.04591836735 Combine like terms: 0.4285714286 + 0.04591836735 = 0.47448979595 0.04591836735 + -0.4285714286x + x2 = 0.47448979595 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = 0.47448979595 Calculate the square root of the right side: 0.688832197 Break this problem into two subproblems by setting (x + -0.2142857143) equal to 0.688832197 and -0.688832197.Subproblem 1
x + -0.2142857143 = 0.688832197 Simplifying x + -0.2142857143 = 0.688832197 Reorder the terms: -0.2142857143 + x = 0.688832197 Solving -0.2142857143 + x = 0.688832197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = 0.688832197 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = 0.688832197 + 0.2142857143 x = 0.688832197 + 0.2142857143 Combine like terms: 0.688832197 + 0.2142857143 = 0.9031179113 x = 0.9031179113 Simplifying x = 0.9031179113Subproblem 2
x + -0.2142857143 = -0.688832197 Simplifying x + -0.2142857143 = -0.688832197 Reorder the terms: -0.2142857143 + x = -0.688832197 Solving -0.2142857143 + x = -0.688832197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = -0.688832197 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = -0.688832197 + 0.2142857143 x = -0.688832197 + 0.2142857143 Combine like terms: -0.688832197 + 0.2142857143 = -0.4745464827 x = -0.4745464827 Simplifying x = -0.4745464827Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9031179113, -0.4745464827}
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