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Simplifying x(308x + -736) = 3892 Reorder the terms: x(-736 + 308x) = 3892 (-736 * x + 308x * x) = 3892 (-736x + 308x2) = 3892 Solving -736x + 308x2 = 3892 Solving for variable 'x'. Reorder the terms: -3892 + -736x + 308x2 = 3892 + -3892 Combine like terms: 3892 + -3892 = 0 -3892 + -736x + 308x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-973 + -184x + 77x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-973 + -184x + 77x2)' equal to zero and attempt to solve: Simplifying -973 + -184x + 77x2 = 0 Solving -973 + -184x + 77x2 = 0 Begin completing the square. Divide all terms by 77 the coefficient of the squared term: Divide each side by '77'. -12.63636364 + -2.38961039x + x2 = 0 Move the constant term to the right: Add '12.63636364' to each side of the equation. -12.63636364 + -2.38961039x + 12.63636364 + x2 = 0 + 12.63636364 Reorder the terms: -12.63636364 + 12.63636364 + -2.38961039x + x2 = 0 + 12.63636364 Combine like terms: -12.63636364 + 12.63636364 = 0.00000000 0.00000000 + -2.38961039x + x2 = 0 + 12.63636364 -2.38961039x + x2 = 0 + 12.63636364 Combine like terms: 0 + 12.63636364 = 12.63636364 -2.38961039x + x2 = 12.63636364 The x term is -2.38961039x. Take half its coefficient (-1.194805195). Square it (1.427559454) and add it to both sides. Add '1.427559454' to each side of the equation. -2.38961039x + 1.427559454 + x2 = 12.63636364 + 1.427559454 Reorder the terms: 1.427559454 + -2.38961039x + x2 = 12.63636364 + 1.427559454 Combine like terms: 12.63636364 + 1.427559454 = 14.063923094 1.427559454 + -2.38961039x + x2 = 14.063923094 Factor a perfect square on the left side: (x + -1.194805195)(x + -1.194805195) = 14.063923094 Calculate the square root of the right side: 3.750189741 Break this problem into two subproblems by setting (x + -1.194805195) equal to 3.750189741 and -3.750189741.Subproblem 1
x + -1.194805195 = 3.750189741 Simplifying x + -1.194805195 = 3.750189741 Reorder the terms: -1.194805195 + x = 3.750189741 Solving -1.194805195 + x = 3.750189741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.194805195' to each side of the equation. -1.194805195 + 1.194805195 + x = 3.750189741 + 1.194805195 Combine like terms: -1.194805195 + 1.194805195 = 0.000000000 0.000000000 + x = 3.750189741 + 1.194805195 x = 3.750189741 + 1.194805195 Combine like terms: 3.750189741 + 1.194805195 = 4.944994936 x = 4.944994936 Simplifying x = 4.944994936Subproblem 2
x + -1.194805195 = -3.750189741 Simplifying x + -1.194805195 = -3.750189741 Reorder the terms: -1.194805195 + x = -3.750189741 Solving -1.194805195 + x = -3.750189741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.194805195' to each side of the equation. -1.194805195 + 1.194805195 + x = -3.750189741 + 1.194805195 Combine like terms: -1.194805195 + 1.194805195 = 0.000000000 0.000000000 + x = -3.750189741 + 1.194805195 x = -3.750189741 + 1.194805195 Combine like terms: -3.750189741 + 1.194805195 = -2.555384546 x = -2.555384546 Simplifying x = -2.555384546Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.944994936, -2.555384546}Solution
x = {4.944994936, -2.555384546}
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