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Simplifying 0 = -1.093406593 + -1.928571429x + 0.2747252747x2 Solving 0 = -1.093406593 + -1.928571429x + 0.2747252747x2 Solving for variable 'x'. Combine like terms: 0 + 1.093406593 = 1.093406593 1.093406593 + 1.928571429x + -0.2747252747x2 = -1.093406593 + -1.928571429x + 0.2747252747x2 + 1.093406593 + 1.928571429x + -0.2747252747x2 Reorder the terms: 1.093406593 + 1.928571429x + -0.2747252747x2 = -1.093406593 + 1.093406593 + -1.928571429x + 1.928571429x + 0.2747252747x2 + -0.2747252747x2 Combine like terms: -1.093406593 + 1.093406593 = 0.000000000 1.093406593 + 1.928571429x + -0.2747252747x2 = 0.000000000 + -1.928571429x + 1.928571429x + 0.2747252747x2 + -0.2747252747x2 1.093406593 + 1.928571429x + -0.2747252747x2 = -1.928571429x + 1.928571429x + 0.2747252747x2 + -0.2747252747x2 Combine like terms: -1.928571429x + 1.928571429x = 0.000000000 1.093406593 + 1.928571429x + -0.2747252747x2 = 0.000000000 + 0.2747252747x2 + -0.2747252747x2 1.093406593 + 1.928571429x + -0.2747252747x2 = 0.2747252747x2 + -0.2747252747x2 Combine like terms: 0.2747252747x2 + -0.2747252747x2 = 0.0000000000 1.093406593 + 1.928571429x + -0.2747252747x2 = 0.0000000000 Begin completing the square. Divide all terms by -0.2747252747 the coefficient of the squared term: Divide each side by '-0.2747252747'. -3.979999999 + -7.020000002x + x2 = 0 Move the constant term to the right: Add '3.979999999' to each side of the equation. -3.979999999 + -7.020000002x + 3.979999999 + x2 = 0 + 3.979999999 Reorder the terms: -3.979999999 + 3.979999999 + -7.020000002x + x2 = 0 + 3.979999999 Combine like terms: -3.979999999 + 3.979999999 = 0.000000000 0.000000000 + -7.020000002x + x2 = 0 + 3.979999999 -7.020000002x + x2 = 0 + 3.979999999 Combine like terms: 0 + 3.979999999 = 3.979999999 -7.020000002x + x2 = 3.979999999 The x term is -7.020000002x. Take half its coefficient (-3.510000001). Square it (12.32010001) and add it to both sides. Add '12.32010001' to each side of the equation. -7.020000002x + 12.32010001 + x2 = 3.979999999 + 12.32010001 Reorder the terms: 12.32010001 + -7.020000002x + x2 = 3.979999999 + 12.32010001 Combine like terms: 3.979999999 + 12.32010001 = 16.300100009 12.32010001 + -7.020000002x + x2 = 16.300100009 Factor a perfect square on the left side: (x + -3.510000001)(x + -3.510000001) = 16.300100009 Calculate the square root of the right side: 4.037338233 Break this problem into two subproblems by setting (x + -3.510000001) equal to 4.037338233 and -4.037338233.Subproblem 1
x + -3.510000001 = 4.037338233 Simplifying x + -3.510000001 = 4.037338233 Reorder the terms: -3.510000001 + x = 4.037338233 Solving -3.510000001 + x = 4.037338233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.510000001' to each side of the equation. -3.510000001 + 3.510000001 + x = 4.037338233 + 3.510000001 Combine like terms: -3.510000001 + 3.510000001 = 0.000000000 0.000000000 + x = 4.037338233 + 3.510000001 x = 4.037338233 + 3.510000001 Combine like terms: 4.037338233 + 3.510000001 = 7.547338234 x = 7.547338234 Simplifying x = 7.547338234Subproblem 2
x + -3.510000001 = -4.037338233 Simplifying x + -3.510000001 = -4.037338233 Reorder the terms: -3.510000001 + x = -4.037338233 Solving -3.510000001 + x = -4.037338233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.510000001' to each side of the equation. -3.510000001 + 3.510000001 + x = -4.037338233 + 3.510000001 Combine like terms: -3.510000001 + 3.510000001 = 0.000000000 0.000000000 + x = -4.037338233 + 3.510000001 x = -4.037338233 + 3.510000001 Combine like terms: -4.037338233 + 3.510000001 = -0.527338232 x = -0.527338232 Simplifying x = -0.527338232Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.547338234, -0.527338232}
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