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Simplifying 36x2 + 7x + -6 = 0 Reorder the terms: -6 + 7x + 36x2 = 0 Solving -6 + 7x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.1666666667 + 0.1944444444x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1944444444x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + 0.1944444444x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + 0.1944444444x + x2 = 0 + 0.1666666667 0.1944444444x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 0.1944444444x + x2 = 0.1666666667 The x term is 0.1944444444x. Take half its coefficient (0.0972222222). Square it (0.009452160490) and add it to both sides. Add '0.009452160490' to each side of the equation. 0.1944444444x + 0.009452160490 + x2 = 0.1666666667 + 0.009452160490 Reorder the terms: 0.009452160490 + 0.1944444444x + x2 = 0.1666666667 + 0.009452160490 Combine like terms: 0.1666666667 + 0.009452160490 = 0.17611882719 0.009452160490 + 0.1944444444x + x2 = 0.17611882719 Factor a perfect square on the left side: (x + 0.0972222222)(x + 0.0972222222) = 0.17611882719 Calculate the square root of the right side: 0.419665137 Break this problem into two subproblems by setting (x + 0.0972222222) equal to 0.419665137 and -0.419665137.Subproblem 1
x + 0.0972222222 = 0.419665137 Simplifying x + 0.0972222222 = 0.419665137 Reorder the terms: 0.0972222222 + x = 0.419665137 Solving 0.0972222222 + x = 0.419665137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0972222222' to each side of the equation. 0.0972222222 + -0.0972222222 + x = 0.419665137 + -0.0972222222 Combine like terms: 0.0972222222 + -0.0972222222 = 0.0000000000 0.0000000000 + x = 0.419665137 + -0.0972222222 x = 0.419665137 + -0.0972222222 Combine like terms: 0.419665137 + -0.0972222222 = 0.3224429148 x = 0.3224429148 Simplifying x = 0.3224429148Subproblem 2
x + 0.0972222222 = -0.419665137 Simplifying x + 0.0972222222 = -0.419665137 Reorder the terms: 0.0972222222 + x = -0.419665137 Solving 0.0972222222 + x = -0.419665137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0972222222' to each side of the equation. 0.0972222222 + -0.0972222222 + x = -0.419665137 + -0.0972222222 Combine like terms: 0.0972222222 + -0.0972222222 = 0.0000000000 0.0000000000 + x = -0.419665137 + -0.0972222222 x = -0.419665137 + -0.0972222222 Combine like terms: -0.419665137 + -0.0972222222 = -0.5168873592 x = -0.5168873592 Simplifying x = -0.5168873592Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3224429148, -0.5168873592}
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