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Simplifying 5x2 + -90x + 365 = 0 Reorder the terms: 365 + -90x + 5x2 = 0 Solving 365 + -90x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(73 + -18x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(73 + -18x + x2)' equal to zero and attempt to solve: Simplifying 73 + -18x + x2 = 0 Solving 73 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-73' to each side of the equation. 73 + -18x + -73 + x2 = 0 + -73 Reorder the terms: 73 + -73 + -18x + x2 = 0 + -73 Combine like terms: 73 + -73 = 0 0 + -18x + x2 = 0 + -73 -18x + x2 = 0 + -73 Combine like terms: 0 + -73 = -73 -18x + x2 = -73 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -73 + 81 Reorder the terms: 81 + -18x + x2 = -73 + 81 Combine like terms: -73 + 81 = 8 81 + -18x + x2 = 8 Factor a perfect square on the left side: (x + -9)(x + -9) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + -9) equal to 2.828427125 and -2.828427125.Subproblem 1
x + -9 = 2.828427125 Simplifying x + -9 = 2.828427125 Reorder the terms: -9 + x = 2.828427125 Solving -9 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 2.828427125 + 9 Combine like terms: -9 + 9 = 0 0 + x = 2.828427125 + 9 x = 2.828427125 + 9 Combine like terms: 2.828427125 + 9 = 11.828427125 x = 11.828427125 Simplifying x = 11.828427125Subproblem 2
x + -9 = -2.828427125 Simplifying x + -9 = -2.828427125 Reorder the terms: -9 + x = -2.828427125 Solving -9 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -2.828427125 + 9 Combine like terms: -9 + 9 = 0 0 + x = -2.828427125 + 9 x = -2.828427125 + 9 Combine like terms: -2.828427125 + 9 = 6.171572875 x = 6.171572875 Simplifying x = 6.171572875Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.828427125, 6.171572875}Solution
x = {11.828427125, 6.171572875}
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