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Simplifying 7x2 + 2.2x + -2 = 0 Reorder the terms: -2 + 2.2x + 7x2 = 0 Solving -2 + 2.2x + 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 + 0.3142857143x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.3142857143x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 0.3142857143x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 0.3142857143x + x2 = 0 + 0.2857142857 0.3142857143x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 0.3142857143x + x2 = 0.2857142857 The x term is 0.3142857143x. Take half its coefficient (0.1571428572). Square it (0.02469387757) and add it to both sides. Add '0.02469387757' to each side of the equation. 0.3142857143x + 0.02469387757 + x2 = 0.2857142857 + 0.02469387757 Reorder the terms: 0.02469387757 + 0.3142857143x + x2 = 0.2857142857 + 0.02469387757 Combine like terms: 0.2857142857 + 0.02469387757 = 0.31040816327 0.02469387757 + 0.3142857143x + x2 = 0.31040816327 Factor a perfect square on the left side: (x + 0.1571428572)(x + 0.1571428572) = 0.31040816327 Calculate the square root of the right side: 0.557142857 Break this problem into two subproblems by setting (x + 0.1571428572) equal to 0.557142857 and -0.557142857.Subproblem 1
x + 0.1571428572 = 0.557142857 Simplifying x + 0.1571428572 = 0.557142857 Reorder the terms: 0.1571428572 + x = 0.557142857 Solving 0.1571428572 + x = 0.557142857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1571428572' to each side of the equation. 0.1571428572 + -0.1571428572 + x = 0.557142857 + -0.1571428572 Combine like terms: 0.1571428572 + -0.1571428572 = 0.0000000000 0.0000000000 + x = 0.557142857 + -0.1571428572 x = 0.557142857 + -0.1571428572 Combine like terms: 0.557142857 + -0.1571428572 = 0.3999999998 x = 0.3999999998 Simplifying x = 0.3999999998Subproblem 2
x + 0.1571428572 = -0.557142857 Simplifying x + 0.1571428572 = -0.557142857 Reorder the terms: 0.1571428572 + x = -0.557142857 Solving 0.1571428572 + x = -0.557142857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1571428572' to each side of the equation. 0.1571428572 + -0.1571428572 + x = -0.557142857 + -0.1571428572 Combine like terms: 0.1571428572 + -0.1571428572 = 0.0000000000 0.0000000000 + x = -0.557142857 + -0.1571428572 x = -0.557142857 + -0.1571428572 Combine like terms: -0.557142857 + -0.1571428572 = -0.7142857142 x = -0.7142857142 Simplifying x = -0.7142857142Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3999999998, -0.7142857142}
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