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Simplifying -1.4x2 + 1.2x + 0.2 = 0 Reorder the terms: 0.2 + 1.2x + -1.4x2 = 0 Solving 0.2 + 1.2x + -1.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.4 the coefficient of the squared term: Divide each side by '-1.4'. -0.1428571429 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -0.8571428571x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -0.8571428571x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -0.8571428571x + x2 = 0 + 0.1428571429 -0.8571428571x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -0.8571428571x + x2 = 0.1428571429 The x term is -0.8571428571x. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571x + 0.1836734694 + x2 = 0.1428571429 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 0.1428571429 + 0.1836734694 Combine like terms: 0.1428571429 + 0.1836734694 = 0.3265306123 0.1836734694 + -0.8571428571x + x2 = 0.3265306123 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 0.3265306123 Calculate the square root of the right side: 0.571428571 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 0.571428571 and -0.571428571.Subproblem 1
x + -0.4285714286 = 0.571428571 Simplifying x + -0.4285714286 = 0.571428571 Reorder the terms: -0.4285714286 + x = 0.571428571 Solving -0.4285714286 + x = 0.571428571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = 0.571428571 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 0.571428571 + 0.4285714286 x = 0.571428571 + 0.4285714286 Combine like terms: 0.571428571 + 0.4285714286 = 0.9999999996 x = 0.9999999996 Simplifying x = 0.9999999996Subproblem 2
x + -0.4285714286 = -0.571428571 Simplifying x + -0.4285714286 = -0.571428571 Reorder the terms: -0.4285714286 + x = -0.571428571 Solving -0.4285714286 + x = -0.571428571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = -0.571428571 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -0.571428571 + 0.4285714286 x = -0.571428571 + 0.4285714286 Combine like terms: -0.571428571 + 0.4285714286 = -0.1428571424 x = -0.1428571424 Simplifying x = -0.1428571424Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9999999996, -0.1428571424}
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