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Simplifying 7x2 = 7 + -3x Solving 7x2 = 7 + -3x Solving for variable 'x'. Reorder the terms: -7 + 3x + 7x2 = 7 + -3x + -7 + 3x Reorder the terms: -7 + 3x + 7x2 = 7 + -7 + -3x + 3x Combine like terms: 7 + -7 = 0 -7 + 3x + 7x2 = 0 + -3x + 3x -7 + 3x + 7x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -7 + 3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.4285714286x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.4285714286x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.4285714286x + x2 = 0 + 1 0.4285714286x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.4285714286x + x2 = 1 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 = 1 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 1 + 0.04591836735 Combine like terms: 1 + 0.04591836735 = 1.04591836735 0.04591836735 + 0.4285714286x + x2 = 1.04591836735 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 1.04591836735 Calculate the square root of the right side: 1.022701505 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 1.022701505 and -1.022701505.Subproblem 1
x + 0.2142857143 = 1.022701505 Simplifying x + 0.2142857143 = 1.022701505 Reorder the terms: 0.2142857143 + x = 1.022701505 Solving 0.2142857143 + x = 1.022701505 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 = 1.022701505 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 1.022701505 + -0.2142857143 x = 1.022701505 + -0.2142857143 Combine like terms: 1.022701505 + -0.2142857143 = 0.8084157907 x = 0.8084157907 Simplifying x = 0.8084157907Subproblem 2
x + 0.2142857143 = -1.022701505 Simplifying x + 0.2142857143 = -1.022701505 Reorder the terms: 0.2142857143 + x = -1.022701505 Solving 0.2142857143 + x = -1.022701505 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 = -1.022701505 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -1.022701505 + -0.2142857143 x = -1.022701505 + -0.2142857143 Combine like terms: -1.022701505 + -0.2142857143 = -1.2369872193 x = -1.2369872193 Simplifying x = -1.2369872193Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8084157907, -1.2369872193}
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