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Simplifying 0.4x + -0.7x2 = -2 Solving 0.4x + -0.7x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + 0.4x + -0.7x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 0.4x + -0.7x2 = 0 Begin completing the square. Divide all terms by -0.7 the coefficient of the squared term: Divide each side by '-0.7'. -2.857142857 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + -0.5714285714x + 2.857142857 + x2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + -0.5714285714x + x2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + -0.5714285714x + x2 = 0 + 2.857142857 -0.5714285714x + x2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 -0.5714285714x + x2 = 2.857142857 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 2.857142857 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 2.857142857 + 0.08163265305 Combine like terms: 2.857142857 + 0.08163265305 = 2.93877551005 0.08163265305 + -0.5714285714x + x2 = 2.93877551005 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 2.93877551005 Calculate the square root of the right side: 1.714285714 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 1.714285714 and -1.714285714.Subproblem 1
x + -0.2857142857 = 1.714285714 Simplifying x + -0.2857142857 = 1.714285714 Reorder the terms: -0.2857142857 + x = 1.714285714 Solving -0.2857142857 + x = 1.714285714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 1.714285714 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 1.714285714 + 0.2857142857 x = 1.714285714 + 0.2857142857 Combine like terms: 1.714285714 + 0.2857142857 = 1.9999999997 x = 1.9999999997 Simplifying x = 1.9999999997Subproblem 2
x + -0.2857142857 = -1.714285714 Simplifying x + -0.2857142857 = -1.714285714 Reorder the terms: -0.2857142857 + x = -1.714285714 Solving -0.2857142857 + x = -1.714285714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -1.714285714 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -1.714285714 + 0.2857142857 x = -1.714285714 + 0.2857142857 Combine like terms: -1.714285714 + 0.2857142857 = -1.4285714283 x = -1.4285714283 Simplifying x = -1.4285714283Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9999999997, -1.4285714283}
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