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Simplifying 7x2 + -2 + 3x = 0 Reorder the terms: -2 + 3x + 7x2 = 0 Solving -2 + 3x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.4285714286x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 0.4285714286x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 0.4285714286x + x2 = 0 + 0.2857142857 0.4285714286x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 0.4285714286x + x2 = 0.2857142857 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 = 0.2857142857 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 0.2857142857 + 0.04591836735 Combine like terms: 0.2857142857 + 0.04591836735 = 0.33163265305 0.04591836735 + 0.4285714286x + x2 = 0.33163265305 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 0.33163265305 Calculate the square root of the right side: 0.575875553 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 0.575875553 and -0.575875553.Subproblem 1
x + 0.2142857143 = 0.575875553 Simplifying x + 0.2142857143 = 0.575875553 Reorder the terms: 0.2142857143 + x = 0.575875553 Solving 0.2142857143 + x = 0.575875553 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 = 0.575875553 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 0.575875553 + -0.2142857143 x = 0.575875553 + -0.2142857143 Combine like terms: 0.575875553 + -0.2142857143 = 0.3615898387 x = 0.3615898387 Simplifying x = 0.3615898387Subproblem 2
x + 0.2142857143 = -0.575875553 Simplifying x + 0.2142857143 = -0.575875553 Reorder the terms: 0.2142857143 + x = -0.575875553 Solving 0.2142857143 + x = -0.575875553 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 = -0.575875553 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -0.575875553 + -0.2142857143 x = -0.575875553 + -0.2142857143 Combine like terms: -0.575875553 + -0.2142857143 = -0.7901612673 x = -0.7901612673 Simplifying x = -0.7901612673Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3615898387, -0.7901612673}
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