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Simplifying 5x2 + 5x + 6 = 180 Reorder the terms: 6 + 5x + 5x2 = 180 Solving 6 + 5x + 5x2 = 180 Solving for variable 'x'. Reorder the terms: 6 + -180 + 5x + 5x2 = 180 + -180 Combine like terms: 6 + -180 = -174 -174 + 5x + 5x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -174 + 5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -34.8 + x + x2 = 0 Move the constant term to the right: Add '34.8' to each side of the equation. -34.8 + x + 34.8 + x2 = 0 + 34.8 Reorder the terms: -34.8 + 34.8 + x + x2 = 0 + 34.8 Combine like terms: -34.8 + 34.8 = 0.0 0.0 + x + x2 = 0 + 34.8 x + x2 = 0 + 34.8 Combine like terms: 0 + 34.8 = 34.8 x + x2 = 34.8 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 = 34.8 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 34.8 + 0.25 Combine like terms: 34.8 + 0.25 = 35.05 1.25 + x2 = 35.05 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 35.05 Calculate the square root of the right side: 5.920304046 Break this problem into two subproblems by setting (x + 0.5) equal to 5.920304046 and -5.920304046.Subproblem 1
x + 0.5 = 5.920304046 Simplifying x + 0.5 = 5.920304046 Reorder the terms: 0.5 + x = 5.920304046 Solving 0.5 + x = 5.920304046 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 = 5.920304046 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.920304046 + -0.5 x = 5.920304046 + -0.5 Combine like terms: 5.920304046 + -0.5 = 5.420304046 x = 5.420304046 Simplifying x = 5.420304046Subproblem 2
x + 0.5 = -5.920304046 Simplifying x + 0.5 = -5.920304046 Reorder the terms: 0.5 + x = -5.920304046 Solving 0.5 + x = -5.920304046 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 = -5.920304046 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.920304046 + -0.5 x = -5.920304046 + -0.5 Combine like terms: -5.920304046 + -0.5 = -6.420304046 x = -6.420304046 Simplifying x = -6.420304046Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.420304046, -6.420304046}
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