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Simplifying 36x2 + 7x + -9 = 0 Reorder the terms: -9 + 7x + 36x2 = 0 Solving -9 + 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'. -0.25 + 0.1944444444x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 0.1944444444x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 0.1944444444x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 0.1944444444x + x2 = 0 + 0.25 0.1944444444x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 0.1944444444x + x2 = 0.25 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 = 0.25 + 0.009452160490 Reorder the terms: 0.009452160490 + 0.1944444444x + x2 = 0.25 + 0.009452160490 Combine like terms: 0.25 + 0.009452160490 = 0.25945216049 0.009452160490 + 0.1944444444x + x2 = 0.25945216049 Factor a perfect square on the left side: (x + 0.0972222222)(x + 0.0972222222) = 0.25945216049 Calculate the square root of the right side: 0.509364467 Break this problem into two subproblems by setting (x + 0.0972222222) equal to 0.509364467 and -0.509364467.Subproblem 1
x + 0.0972222222 = 0.509364467 Simplifying x + 0.0972222222 = 0.509364467 Reorder the terms: 0.0972222222 + x = 0.509364467 Solving 0.0972222222 + x = 0.509364467 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 = 0.509364467 + -0.0972222222 Combine like terms: 0.0972222222 + -0.0972222222 = 0.0000000000 0.0000000000 + x = 0.509364467 + -0.0972222222 x = 0.509364467 + -0.0972222222 Combine like terms: 0.509364467 + -0.0972222222 = 0.4121422448 x = 0.4121422448 Simplifying x = 0.4121422448Subproblem 2
x + 0.0972222222 = -0.509364467 Simplifying x + 0.0972222222 = -0.509364467 Reorder the terms: 0.0972222222 + x = -0.509364467 Solving 0.0972222222 + x = -0.509364467 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 = -0.509364467 + -0.0972222222 Combine like terms: 0.0972222222 + -0.0972222222 = 0.0000000000 0.0000000000 + x = -0.509364467 + -0.0972222222 x = -0.509364467 + -0.0972222222 Combine like terms: -0.509364467 + -0.0972222222 = -0.6065866892 x = -0.6065866892 Simplifying x = -0.6065866892Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4121422448, -0.6065866892}
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