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Simplifying 0 = 7x2 + -3x + -2 Reorder the terms: 0 = -2 + -3x + 7x2 Solving 0 = -2 + -3x + 7x2 Solving for variable 'x'. Combine like terms: 0 + 2 = 2 2 + 3x + -7x2 = -2 + -3x + 7x2 + 2 + 3x + -7x2 Reorder the terms: 2 + 3x + -7x2 = -2 + 2 + -3x + 3x + 7x2 + -7x2 Combine like terms: -2 + 2 = 0 2 + 3x + -7x2 = 0 + -3x + 3x + 7x2 + -7x2 2 + 3x + -7x2 = -3x + 3x + 7x2 + -7x2 Combine like terms: -3x + 3x = 0 2 + 3x + -7x2 = 0 + 7x2 + -7x2 2 + 3x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 2 + 3x + -7x2 = 0 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 = 0.7901612673 x = 0.7901612673 Simplifying x = 0.7901612673Subproblem 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 = -0.3615898387 x = -0.3615898387 Simplifying x = -0.3615898387Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7901612673, -0.3615898387}
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