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Simplifying 6x2 + 17x + -63 = 0 Reorder the terms: -63 + 17x + 6x2 = 0 Solving -63 + 17x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -10.5 + 2.833333333x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 2.833333333x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 2.833333333x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 2.833333333x + x2 = 0 + 10.5 2.833333333x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 2.833333333x + x2 = 10.5 The x term is 2.833333333x. Take half its coefficient (1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. 2.833333333x + 2.006944445 + x2 = 10.5 + 2.006944445 Reorder the terms: 2.006944445 + 2.833333333x + x2 = 10.5 + 2.006944445 Combine like terms: 10.5 + 2.006944445 = 12.506944445 2.006944445 + 2.833333333x + x2 = 12.506944445 Factor a perfect square on the left side: (x + 1.416666667)(x + 1.416666667) = 12.506944445 Calculate the square root of the right side: 3.536515862 Break this problem into two subproblems by setting (x + 1.416666667) equal to 3.536515862 and -3.536515862.Subproblem 1
x + 1.416666667 = 3.536515862 Simplifying x + 1.416666667 = 3.536515862 Reorder the terms: 1.416666667 + x = 3.536515862 Solving 1.416666667 + x = 3.536515862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + x = 3.536515862 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + x = 3.536515862 + -1.416666667 x = 3.536515862 + -1.416666667 Combine like terms: 3.536515862 + -1.416666667 = 2.119849195 x = 2.119849195 Simplifying x = 2.119849195Subproblem 2
x + 1.416666667 = -3.536515862 Simplifying x + 1.416666667 = -3.536515862 Reorder the terms: 1.416666667 + x = -3.536515862 Solving 1.416666667 + x = -3.536515862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + x = -3.536515862 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + x = -3.536515862 + -1.416666667 x = -3.536515862 + -1.416666667 Combine like terms: -3.536515862 + -1.416666667 = -4.953182529 x = -4.953182529 Simplifying x = -4.953182529Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.119849195, -4.953182529}
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