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Simplifying 5.0 + 0.2x = 3.5x2 Solving 5.0 + 0.2x = 3.5x2 Solving for variable 'x'. Combine like terms: 3.5x2 + -3.5x2 = 0.0 5.0 + 0.2x + -3.5x2 = 0.0 Begin completing the square. Divide all terms by -3.5 the coefficient of the squared term: Divide each side by '-3.5'. -1.428571429 + -0.05714285714x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -0.05714285714x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -0.05714285714x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -0.05714285714x + x2 = 0 + 1.428571429 -0.05714285714x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -0.05714285714x + x2 = 1.428571429 The x term is -0.05714285714x. Take half its coefficient (-0.02857142857). Square it (0.0008163265305) and add it to both sides. Add '0.0008163265305' to each side of the equation. -0.05714285714x + 0.0008163265305 + x2 = 1.428571429 + 0.0008163265305 Reorder the terms: 0.0008163265305 + -0.05714285714x + x2 = 1.428571429 + 0.0008163265305 Combine like terms: 1.428571429 + 0.0008163265305 = 1.4293877555305 0.0008163265305 + -0.05714285714x + x2 = 1.4293877555305 Factor a perfect square on the left side: (x + -0.02857142857)(x + -0.02857142857) = 1.4293877555305 Calculate the square root of the right side: 1.195570055 Break this problem into two subproblems by setting (x + -0.02857142857) equal to 1.195570055 and -1.195570055.Subproblem 1
x + -0.02857142857 = 1.195570055 Simplifying x + -0.02857142857 = 1.195570055 Reorder the terms: -0.02857142857 + x = 1.195570055 Solving -0.02857142857 + x = 1.195570055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02857142857' to each side of the equation. -0.02857142857 + 0.02857142857 + x = 1.195570055 + 0.02857142857 Combine like terms: -0.02857142857 + 0.02857142857 = 0.00000000000 0.00000000000 + x = 1.195570055 + 0.02857142857 x = 1.195570055 + 0.02857142857 Combine like terms: 1.195570055 + 0.02857142857 = 1.22414148357 x = 1.22414148357 Simplifying x = 1.22414148357Subproblem 2
x + -0.02857142857 = -1.195570055 Simplifying x + -0.02857142857 = -1.195570055 Reorder the terms: -0.02857142857 + x = -1.195570055 Solving -0.02857142857 + x = -1.195570055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02857142857' to each side of the equation. -0.02857142857 + 0.02857142857 + x = -1.195570055 + 0.02857142857 Combine like terms: -0.02857142857 + 0.02857142857 = 0.00000000000 0.00000000000 + x = -1.195570055 + 0.02857142857 x = -1.195570055 + 0.02857142857 Combine like terms: -1.195570055 + 0.02857142857 = -1.16699862643 x = -1.16699862643 Simplifying x = -1.16699862643Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.22414148357, -1.16699862643}
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