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Simplifying 7x2 + -2x + -72 = 0 Reorder the terms: -72 + -2x + 7x2 = 0 Solving -72 + -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'. -10.28571429 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '10.28571429' to each side of the equation. -10.28571429 + -0.2857142857x + 10.28571429 + x2 = 0 + 10.28571429 Reorder the terms: -10.28571429 + 10.28571429 + -0.2857142857x + x2 = 0 + 10.28571429 Combine like terms: -10.28571429 + 10.28571429 = 0.00000000 0.00000000 + -0.2857142857x + x2 = 0 + 10.28571429 -0.2857142857x + x2 = 0 + 10.28571429 Combine like terms: 0 + 10.28571429 = 10.28571429 -0.2857142857x + x2 = 10.28571429 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 = 10.28571429 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 10.28571429 + 0.02040816328 Combine like terms: 10.28571429 + 0.02040816328 = 10.30612245328 0.02040816328 + -0.2857142857x + x2 = 10.30612245328 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 10.30612245328 Calculate the square root of the right side: 3.210315008 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 3.210315008 and -3.210315008.Subproblem 1
x + -0.1428571429 = 3.210315008 Simplifying x + -0.1428571429 = 3.210315008 Reorder the terms: -0.1428571429 + x = 3.210315008 Solving -0.1428571429 + x = 3.210315008 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 = 3.210315008 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 3.210315008 + 0.1428571429 x = 3.210315008 + 0.1428571429 Combine like terms: 3.210315008 + 0.1428571429 = 3.3531721509 x = 3.3531721509 Simplifying x = 3.3531721509Subproblem 2
x + -0.1428571429 = -3.210315008 Simplifying x + -0.1428571429 = -3.210315008 Reorder the terms: -0.1428571429 + x = -3.210315008 Solving -0.1428571429 + x = -3.210315008 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 = -3.210315008 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -3.210315008 + 0.1428571429 x = -3.210315008 + 0.1428571429 Combine like terms: -3.210315008 + 0.1428571429 = -3.0674578651 x = -3.0674578651 Simplifying x = -3.0674578651Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.3531721509, -3.0674578651}
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