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Simplifying 5(2x2 + -59x + 365) = 0 Reorder the terms: 5(365 + -59x + 2x2) = 0 (365 * 5 + -59x * 5 + 2x2 * 5) = 0 (1825 + -295x + 10x2) = 0 Solving 1825 + -295x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(365 + -59x + 2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(365 + -59x + 2x2)' equal to zero and attempt to solve: Simplifying 365 + -59x + 2x2 = 0 Solving 365 + -59x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 182.5 + -29.5x + x2 = 0 Move the constant term to the right: Add '-182.5' to each side of the equation. 182.5 + -29.5x + -182.5 + x2 = 0 + -182.5 Reorder the terms: 182.5 + -182.5 + -29.5x + x2 = 0 + -182.5 Combine like terms: 182.5 + -182.5 = 0.0 0.0 + -29.5x + x2 = 0 + -182.5 -29.5x + x2 = 0 + -182.5 Combine like terms: 0 + -182.5 = -182.5 -29.5x + x2 = -182.5 The x term is -29.5x. Take half its coefficient (-14.75). Square it (217.5625) and add it to both sides. Add '217.5625' to each side of the equation. -29.5x + 217.5625 + x2 = -182.5 + 217.5625 Reorder the terms: 217.5625 + -29.5x + x2 = -182.5 + 217.5625 Combine like terms: -182.5 + 217.5625 = 35.0625 217.5625 + -29.5x + x2 = 35.0625 Factor a perfect square on the left side: (x + -14.75)(x + -14.75) = 35.0625 Calculate the square root of the right side: 5.921359641 Break this problem into two subproblems by setting (x + -14.75) equal to 5.921359641 and -5.921359641.Subproblem 1
x + -14.75 = 5.921359641 Simplifying x + -14.75 = 5.921359641 Reorder the terms: -14.75 + x = 5.921359641 Solving -14.75 + x = 5.921359641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.75' to each side of the equation. -14.75 + 14.75 + x = 5.921359641 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + x = 5.921359641 + 14.75 x = 5.921359641 + 14.75 Combine like terms: 5.921359641 + 14.75 = 20.671359641 x = 20.671359641 Simplifying x = 20.671359641Subproblem 2
x + -14.75 = -5.921359641 Simplifying x + -14.75 = -5.921359641 Reorder the terms: -14.75 + x = -5.921359641 Solving -14.75 + x = -5.921359641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.75' to each side of the equation. -14.75 + 14.75 + x = -5.921359641 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + x = -5.921359641 + 14.75 x = -5.921359641 + 14.75 Combine like terms: -5.921359641 + 14.75 = 8.828640359 x = 8.828640359 Simplifying x = 8.828640359Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.671359641, 8.828640359}Solution
x = {20.671359641, 8.828640359}
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