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Simplifying -145 + -270x + -40x2 = 0 Solving -145 + -270x + -40x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-5'. -5(29 + 54x + 8x2) = 0 Ignore the factor -5.Subproblem 1
Set the factor '(29 + 54x + 8x2)' equal to zero and attempt to solve: Simplifying 29 + 54x + 8x2 = 0 Solving 29 + 54x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 3.625 + 6.75x + x2 = 0 Move the constant term to the right: Add '-3.625' to each side of the equation. 3.625 + 6.75x + -3.625 + x2 = 0 + -3.625 Reorder the terms: 3.625 + -3.625 + 6.75x + x2 = 0 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + 6.75x + x2 = 0 + -3.625 6.75x + x2 = 0 + -3.625 Combine like terms: 0 + -3.625 = -3.625 6.75x + x2 = -3.625 The x term is 6.75x. Take half its coefficient (3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. 6.75x + 11.390625 + x2 = -3.625 + 11.390625 Reorder the terms: 11.390625 + 6.75x + x2 = -3.625 + 11.390625 Combine like terms: -3.625 + 11.390625 = 7.765625 11.390625 + 6.75x + x2 = 7.765625 Factor a perfect square on the left side: (x + 3.375)(x + 3.375) = 7.765625 Calculate the square root of the right side: 2.786687101 Break this problem into two subproblems by setting (x + 3.375) equal to 2.786687101 and -2.786687101.Subproblem 1
x + 3.375 = 2.786687101 Simplifying x + 3.375 = 2.786687101 Reorder the terms: 3.375 + x = 2.786687101 Solving 3.375 + x = 2.786687101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = 2.786687101 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = 2.786687101 + -3.375 x = 2.786687101 + -3.375 Combine like terms: 2.786687101 + -3.375 = -0.588312899 x = -0.588312899 Simplifying x = -0.588312899Subproblem 2
x + 3.375 = -2.786687101 Simplifying x + 3.375 = -2.786687101 Reorder the terms: 3.375 + x = -2.786687101 Solving 3.375 + x = -2.786687101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = -2.786687101 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = -2.786687101 + -3.375 x = -2.786687101 + -3.375 Combine like terms: -2.786687101 + -3.375 = -6.161687101 x = -6.161687101 Simplifying x = -6.161687101Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.588312899, -6.161687101}Solution
x = {-0.588312899, -6.161687101}
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