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Simplifying 7x2 + -3x = 7 Reorder the terms: -3x + 7x2 = 7 Solving -3x + 7x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -3x + 7x2 = 7 + -7 Combine like terms: 7 + -7 = 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 = 1.2369872193 x = 1.2369872193 Simplifying x = 1.2369872193Subproblem 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 = -0.8084157907 x = -0.8084157907 Simplifying x = -0.8084157907Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2369872193, -0.8084157907}
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