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Simplifying 50 = -16x2 + 96x Reorder the terms: 50 = 96x + -16x2 Solving 50 = 96x + -16x2 Solving for variable 'x'. Reorder the terms: 50 + -96x + 16x2 = 96x + -96x + -16x2 + 16x2 Combine like terms: 96x + -96x = 0 50 + -96x + 16x2 = 0 + -16x2 + 16x2 50 + -96x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 50 + -96x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -48x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + -48x + 8x2)' equal to zero and attempt to solve: Simplifying 25 + -48x + 8x2 = 0 Solving 25 + -48x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 3.125 + -6x + x2 = 0 Move the constant term to the right: Add '-3.125' to each side of the equation. 3.125 + -6x + -3.125 + x2 = 0 + -3.125 Reorder the terms: 3.125 + -3.125 + -6x + x2 = 0 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + -6x + x2 = 0 + -3.125 -6x + x2 = 0 + -3.125 Combine like terms: 0 + -3.125 = -3.125 -6x + x2 = -3.125 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -3.125 + 9 Reorder the terms: 9 + -6x + x2 = -3.125 + 9 Combine like terms: -3.125 + 9 = 5.875 9 + -6x + x2 = 5.875 Factor a perfect square on the left side: (x + -3)(x + -3) = 5.875 Calculate the square root of the right side: 2.423839929 Break this problem into two subproblems by setting (x + -3) equal to 2.423839929 and -2.423839929.Subproblem 1
x + -3 = 2.423839929 Simplifying x + -3 = 2.423839929 Reorder the terms: -3 + x = 2.423839929 Solving -3 + x = 2.423839929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.423839929 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.423839929 + 3 x = 2.423839929 + 3 Combine like terms: 2.423839929 + 3 = 5.423839929 x = 5.423839929 Simplifying x = 5.423839929Subproblem 2
x + -3 = -2.423839929 Simplifying x + -3 = -2.423839929 Reorder the terms: -3 + x = -2.423839929 Solving -3 + x = -2.423839929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.423839929 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.423839929 + 3 x = -2.423839929 + 3 Combine like terms: -2.423839929 + 3 = 0.576160071 x = 0.576160071 Simplifying x = 0.576160071Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.423839929, 0.576160071}Solution
x = {5.423839929, 0.576160071}
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