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Simplifying -36 + -14x + 49x2 = 0 Solving -36 + -14x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.7346938776 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.7346938776' to each side of the equation. -0.7346938776 + -0.2857142857x + 0.7346938776 + x2 = 0 + 0.7346938776 Reorder the terms: -0.7346938776 + 0.7346938776 + -0.2857142857x + x2 = 0 + 0.7346938776 Combine like terms: -0.7346938776 + 0.7346938776 = 0.0000000000 0.0000000000 + -0.2857142857x + x2 = 0 + 0.7346938776 -0.2857142857x + x2 = 0 + 0.7346938776 Combine like terms: 0 + 0.7346938776 = 0.7346938776 -0.2857142857x + x2 = 0.7346938776 The x term is -0.2857142857x. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857x + 0.02040816328 + x2 = 0.7346938776 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 0.7346938776 + 0.02040816328 Combine like terms: 0.7346938776 + 0.02040816328 = 0.75510204088 0.02040816328 + -0.2857142857x + x2 = 0.75510204088 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 0.75510204088 Calculate the square root of the right side: 0.868966076 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 0.868966076 and -0.868966076.Subproblem 1
x + -0.1428571429 = 0.868966076 Simplifying x + -0.1428571429 = 0.868966076 Reorder the terms: -0.1428571429 + x = 0.868966076 Solving -0.1428571429 + x = 0.868966076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = 0.868966076 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 0.868966076 + 0.1428571429 x = 0.868966076 + 0.1428571429 Combine like terms: 0.868966076 + 0.1428571429 = 1.0118232189 x = 1.0118232189 Simplifying x = 1.0118232189Subproblem 2
x + -0.1428571429 = -0.868966076 Simplifying x + -0.1428571429 = -0.868966076 Reorder the terms: -0.1428571429 + x = -0.868966076 Solving -0.1428571429 + x = -0.868966076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = -0.868966076 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -0.868966076 + 0.1428571429 x = -0.868966076 + 0.1428571429 Combine like terms: -0.868966076 + 0.1428571429 = -0.7261089331 x = -0.7261089331 Simplifying x = -0.7261089331Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0118232189, -0.7261089331}
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