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Simplifying 180x2 + 35x + -180 = 0 Reorder the terms: -180 + 35x + 180x2 = 0 Solving -180 + 35x + 180x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-36 + 7x + 36x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-36 + 7x + 36x2)' equal to zero and attempt to solve: Simplifying -36 + 7x + 36x2 = 0 Solving -36 + 7x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -1 + 0.1944444444x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.1944444444x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.1944444444x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.1944444444x + x2 = 0 + 1 0.1944444444x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.1944444444x + x2 = 1 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 = 1 + 0.009452160490 Reorder the terms: 0.009452160490 + 0.1944444444x + x2 = 1 + 0.009452160490 Combine like terms: 1 + 0.009452160490 = 1.00945216049 0.009452160490 + 0.1944444444x + x2 = 1.00945216049 Factor a perfect square on the left side: (x + 0.0972222222)(x + 0.0972222222) = 1.00945216049 Calculate the square root of the right side: 1.004714965 Break this problem into two subproblems by setting (x + 0.0972222222) equal to 1.004714965 and -1.004714965.Subproblem 1
x + 0.0972222222 = 1.004714965 Simplifying x + 0.0972222222 = 1.004714965 Reorder the terms: 0.0972222222 + x = 1.004714965 Solving 0.0972222222 + x = 1.004714965 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 = 1.004714965 + -0.0972222222 Combine like terms: 0.0972222222 + -0.0972222222 = 0.0000000000 0.0000000000 + x = 1.004714965 + -0.0972222222 x = 1.004714965 + -0.0972222222 Combine like terms: 1.004714965 + -0.0972222222 = 0.9074927428 x = 0.9074927428 Simplifying x = 0.9074927428Subproblem 2
x + 0.0972222222 = -1.004714965 Simplifying x + 0.0972222222 = -1.004714965 Reorder the terms: 0.0972222222 + x = -1.004714965 Solving 0.0972222222 + x = -1.004714965 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 = -1.004714965 + -0.0972222222 Combine like terms: 0.0972222222 + -0.0972222222 = 0.0000000000 0.0000000000 + x = -1.004714965 + -0.0972222222 x = -1.004714965 + -0.0972222222 Combine like terms: -1.004714965 + -0.0972222222 = -1.1019371872 x = -1.1019371872 Simplifying x = -1.1019371872Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9074927428, -1.1019371872}Solution
x = {0.9074927428, -1.1019371872}
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