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Simplifying 2x2 + 7x + 6 = 180 Reorder the terms: 6 + 7x + 2x2 = 180 Solving 6 + 7x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: 6 + -180 + 7x + 2x2 = 180 + -180 Combine like terms: 6 + -180 = -174 -174 + 7x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -174 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -87 + 3.5x + x2 = 0 Move the constant term to the right: Add '87' to each side of the equation. -87 + 3.5x + 87 + x2 = 0 + 87 Reorder the terms: -87 + 87 + 3.5x + x2 = 0 + 87 Combine like terms: -87 + 87 = 0 0 + 3.5x + x2 = 0 + 87 3.5x + x2 = 0 + 87 Combine like terms: 0 + 87 = 87 3.5x + x2 = 87 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 87 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 87 + 3.0625 Combine like terms: 87 + 3.0625 = 90.0625 3.0625 + 3.5x + x2 = 90.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 90.0625 Calculate the square root of the right side: 9.490126448 Break this problem into two subproblems by setting (x + 1.75) equal to 9.490126448 and -9.490126448.Subproblem 1
x + 1.75 = 9.490126448 Simplifying x + 1.75 = 9.490126448 Reorder the terms: 1.75 + x = 9.490126448 Solving 1.75 + x = 9.490126448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 9.490126448 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 9.490126448 + -1.75 x = 9.490126448 + -1.75 Combine like terms: 9.490126448 + -1.75 = 7.740126448 x = 7.740126448 Simplifying x = 7.740126448Subproblem 2
x + 1.75 = -9.490126448 Simplifying x + 1.75 = -9.490126448 Reorder the terms: 1.75 + x = -9.490126448 Solving 1.75 + x = -9.490126448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -9.490126448 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -9.490126448 + -1.75 x = -9.490126448 + -1.75 Combine like terms: -9.490126448 + -1.75 = -11.240126448 x = -11.240126448 Simplifying x = -11.240126448Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.740126448, -11.240126448}
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