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Simplifying 48x2 + 16x + -18800 = 0 Reorder the terms: -18800 + 16x + 48x2 = 0 Solving -18800 + 16x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(-1175 + x + 3x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-1175 + x + 3x2)' equal to zero and attempt to solve: Simplifying -1175 + x + 3x2 = 0 Solving -1175 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -391.6666667 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '391.6666667' to each side of the equation. -391.6666667 + 0.3333333333x + 391.6666667 + x2 = 0 + 391.6666667 Reorder the terms: -391.6666667 + 391.6666667 + 0.3333333333x + x2 = 0 + 391.6666667 Combine like terms: -391.6666667 + 391.6666667 = 0.0000000 0.0000000 + 0.3333333333x + x2 = 0 + 391.6666667 0.3333333333x + x2 = 0 + 391.6666667 Combine like terms: 0 + 391.6666667 = 391.6666667 0.3333333333x + x2 = 391.6666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = 391.6666667 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = 391.6666667 + 0.25 Combine like terms: 391.6666667 + 0.25 = 391.9166667 0.25 + 0.3333333333x + x2 = 391.9166667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 391.9166667 Calculate the square root of the right side: 19.796885278 Break this problem into two subproblems by setting (x + 0.5) equal to 19.796885278 and -19.796885278.Subproblem 1
x + 0.5 = 19.796885278 Simplifying x + 0.5 = 19.796885278 Reorder the terms: 0.5 + x = 19.796885278 Solving 0.5 + x = 19.796885278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 19.796885278 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 19.796885278 + -0.5 x = 19.796885278 + -0.5 Combine like terms: 19.796885278 + -0.5 = 19.296885278 x = 19.296885278 Simplifying x = 19.296885278Subproblem 2
x + 0.5 = -19.796885278 Simplifying x + 0.5 = -19.796885278 Reorder the terms: 0.5 + x = -19.796885278 Solving 0.5 + x = -19.796885278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -19.796885278 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -19.796885278 + -0.5 x = -19.796885278 + -0.5 Combine like terms: -19.796885278 + -0.5 = -20.296885278 x = -20.296885278 Simplifying x = -20.296885278Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.296885278, -20.296885278}Solution
x = {19.296885278, -20.296885278}
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