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Simplifying 6x2 + 6x = 17 Reorder the terms: 6x + 6x2 = 17 Solving 6x + 6x2 = 17 Solving for variable 'x'. Reorder the terms: -17 + 6x + 6x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 6x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.833333333 + x + x2 = 0 Move the constant term to the right: Add '2.833333333' to each side of the equation. -2.833333333 + x + 2.833333333 + x2 = 0 + 2.833333333 Reorder the terms: -2.833333333 + 2.833333333 + x + x2 = 0 + 2.833333333 Combine like terms: -2.833333333 + 2.833333333 = 0.000000000 0.000000000 + x + x2 = 0 + 2.833333333 x + x2 = 0 + 2.833333333 Combine like terms: 0 + 2.833333333 = 2.833333333 x + x2 = 2.833333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 2.833333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 2.833333333 + 0.25 Combine like terms: 2.833333333 + 0.25 = 3.083333333 1.25 + x2 = 3.083333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3.083333333 Calculate the square root of the right side: 1.755942292 Break this problem into two subproblems by setting (x + 0.5) equal to 1.755942292 and -1.755942292.Subproblem 1
x + 0.5 = 1.755942292 Simplifying x + 0.5 = 1.755942292 Reorder the terms: 0.5 + x = 1.755942292 Solving 0.5 + x = 1.755942292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.755942292 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.755942292 + -0.5 x = 1.755942292 + -0.5 Combine like terms: 1.755942292 + -0.5 = 1.255942292 x = 1.255942292 Simplifying x = 1.255942292Subproblem 2
x + 0.5 = -1.755942292 Simplifying x + 0.5 = -1.755942292 Reorder the terms: 0.5 + x = -1.755942292 Solving 0.5 + x = -1.755942292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.755942292 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.755942292 + -0.5 x = -1.755942292 + -0.5 Combine like terms: -1.755942292 + -0.5 = -2.255942292 x = -2.255942292 Simplifying x = -2.255942292Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.255942292, -2.255942292}
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