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Simplifying 7x2 + -3x + -7 = 7 Reorder the terms: -7 + -3x + 7x2 = 7 Solving -7 + -3x + 7x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -7 + -3x + 7x2 = 7 + -7 Combine like terms: -7 + -7 = -14 -14 + -3x + 7x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -14 + -3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.4285714286x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -0.4285714286x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.4285714286x + x2 = 0 + 2 -0.4285714286x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.4285714286x + x2 = 2 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 = 2 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = 2 + 0.04591836735 Combine like terms: 2 + 0.04591836735 = 2.04591836735 0.04591836735 + -0.4285714286x + x2 = 2.04591836735 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = 2.04591836735 Calculate the square root of the right side: 1.430356028 Break this problem into two subproblems by setting (x + -0.2142857143) equal to 1.430356028 and -1.430356028.Subproblem 1
x + -0.2142857143 = 1.430356028 Simplifying x + -0.2142857143 = 1.430356028 Reorder the terms: -0.2142857143 + x = 1.430356028 Solving -0.2142857143 + x = 1.430356028 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 = 1.430356028 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = 1.430356028 + 0.2142857143 x = 1.430356028 + 0.2142857143 Combine like terms: 1.430356028 + 0.2142857143 = 1.6446417423 x = 1.6446417423 Simplifying x = 1.6446417423Subproblem 2
x + -0.2142857143 = -1.430356028 Simplifying x + -0.2142857143 = -1.430356028 Reorder the terms: -0.2142857143 + x = -1.430356028 Solving -0.2142857143 + x = -1.430356028 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 = -1.430356028 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = -1.430356028 + 0.2142857143 x = -1.430356028 + 0.2142857143 Combine like terms: -1.430356028 + 0.2142857143 = -1.2160703137 x = -1.2160703137 Simplifying x = -1.2160703137Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6446417423, -1.2160703137}
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