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Simplifying -16x2 + 84x = 84 Reorder the terms: 84x + -16x2 = 84 Solving 84x + -16x2 = 84 Solving for variable 'x'. Reorder the terms: -84 + 84x + -16x2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + 84x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-21 + 21x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-21 + 21x + -4x2)' equal to zero and attempt to solve: Simplifying -21 + 21x + -4x2 = 0 Solving -21 + 21x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 5.25 + -5.25x + x2 = 0 Move the constant term to the right: Add '-5.25' to each side of the equation. 5.25 + -5.25x + -5.25 + x2 = 0 + -5.25 Reorder the terms: 5.25 + -5.25 + -5.25x + x2 = 0 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + -5.25x + x2 = 0 + -5.25 -5.25x + x2 = 0 + -5.25 Combine like terms: 0 + -5.25 = -5.25 -5.25x + x2 = -5.25 The x term is -5.25x. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25x + 6.890625 + x2 = -5.25 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = -5.25 + 6.890625 Combine like terms: -5.25 + 6.890625 = 1.640625 6.890625 + -5.25x + x2 = 1.640625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (x + -2.625) equal to 1.280868846 and -1.280868846.Subproblem 1
x + -2.625 = 1.280868846 Simplifying x + -2.625 = 1.280868846 Reorder the terms: -2.625 + x = 1.280868846 Solving -2.625 + x = 1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = 1.280868846 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 1.280868846 + 2.625 x = 1.280868846 + 2.625 Combine like terms: 1.280868846 + 2.625 = 3.905868846 x = 3.905868846 Simplifying x = 3.905868846Subproblem 2
x + -2.625 = -1.280868846 Simplifying x + -2.625 = -1.280868846 Reorder the terms: -2.625 + x = -1.280868846 Solving -2.625 + x = -1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = -1.280868846 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -1.280868846 + 2.625 x = -1.280868846 + 2.625 Combine like terms: -1.280868846 + 2.625 = 1.344131154 x = 1.344131154 Simplifying x = 1.344131154Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.905868846, 1.344131154}Solution
x = {3.905868846, 1.344131154}
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