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Simplifying 360x2 + -340x = 2750 Reorder the terms: -340x + 360x2 = 2750 Solving -340x + 360x2 = 2750 Solving for variable 'x'. Reorder the terms: -2750 + -340x + 360x2 = 2750 + -2750 Combine like terms: 2750 + -2750 = 0 -2750 + -340x + 360x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-275 + -34x + 36x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-275 + -34x + 36x2)' equal to zero and attempt to solve: Simplifying -275 + -34x + 36x2 = 0 Solving -275 + -34x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -7.638888889 + -0.9444444444x + x2 = 0 Move the constant term to the right: Add '7.638888889' to each side of the equation. -7.638888889 + -0.9444444444x + 7.638888889 + x2 = 0 + 7.638888889 Reorder the terms: -7.638888889 + 7.638888889 + -0.9444444444x + x2 = 0 + 7.638888889 Combine like terms: -7.638888889 + 7.638888889 = 0.000000000 0.000000000 + -0.9444444444x + x2 = 0 + 7.638888889 -0.9444444444x + x2 = 0 + 7.638888889 Combine like terms: 0 + 7.638888889 = 7.638888889 -0.9444444444x + x2 = 7.638888889 The x term is -0.9444444444x. Take half its coefficient (-0.4722222222). Square it (0.2229938271) and add it to both sides. Add '0.2229938271' to each side of the equation. -0.9444444444x + 0.2229938271 + x2 = 7.638888889 + 0.2229938271 Reorder the terms: 0.2229938271 + -0.9444444444x + x2 = 7.638888889 + 0.2229938271 Combine like terms: 7.638888889 + 0.2229938271 = 7.8618827161 0.2229938271 + -0.9444444444x + x2 = 7.8618827161 Factor a perfect square on the left side: (x + -0.4722222222)(x + -0.4722222222) = 7.8618827161 Calculate the square root of the right side: 2.803904905 Break this problem into two subproblems by setting (x + -0.4722222222) equal to 2.803904905 and -2.803904905.Subproblem 1
x + -0.4722222222 = 2.803904905 Simplifying x + -0.4722222222 = 2.803904905 Reorder the terms: -0.4722222222 + x = 2.803904905 Solving -0.4722222222 + x = 2.803904905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4722222222' to each side of the equation. -0.4722222222 + 0.4722222222 + x = 2.803904905 + 0.4722222222 Combine like terms: -0.4722222222 + 0.4722222222 = 0.0000000000 0.0000000000 + x = 2.803904905 + 0.4722222222 x = 2.803904905 + 0.4722222222 Combine like terms: 2.803904905 + 0.4722222222 = 3.2761271272 x = 3.2761271272 Simplifying x = 3.2761271272Subproblem 2
x + -0.4722222222 = -2.803904905 Simplifying x + -0.4722222222 = -2.803904905 Reorder the terms: -0.4722222222 + x = -2.803904905 Solving -0.4722222222 + x = -2.803904905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4722222222' to each side of the equation. -0.4722222222 + 0.4722222222 + x = -2.803904905 + 0.4722222222 Combine like terms: -0.4722222222 + 0.4722222222 = 0.0000000000 0.0000000000 + x = -2.803904905 + 0.4722222222 x = -2.803904905 + 0.4722222222 Combine like terms: -2.803904905 + 0.4722222222 = -2.3316826828 x = -2.3316826828 Simplifying x = -2.3316826828Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2761271272, -2.3316826828}Solution
x = {3.2761271272, -2.3316826828}
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