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Simplifying -16x2 + 96x + 200 = 0 Reorder the terms: 200 + 96x + -16x2 = 0 Solving 200 + 96x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(25 + 12x + -2x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(25 + 12x + -2x2)' equal to zero and attempt to solve: Simplifying 25 + 12x + -2x2 = 0 Solving 25 + 12x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -12.5 + -6x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -6x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -6x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -6x + x2 = 0 + 12.5 -6x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -6x + x2 = 12.5 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 = 12.5 + 9 Reorder the terms: 9 + -6x + x2 = 12.5 + 9 Combine like terms: 12.5 + 9 = 21.5 9 + -6x + x2 = 21.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 21.5 Calculate the square root of the right side: 4.636809248 Break this problem into two subproblems by setting (x + -3) equal to 4.636809248 and -4.636809248.Subproblem 1
x + -3 = 4.636809248 Simplifying x + -3 = 4.636809248 Reorder the terms: -3 + x = 4.636809248 Solving -3 + x = 4.636809248 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 = 4.636809248 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.636809248 + 3 x = 4.636809248 + 3 Combine like terms: 4.636809248 + 3 = 7.636809248 x = 7.636809248 Simplifying x = 7.636809248Subproblem 2
x + -3 = -4.636809248 Simplifying x + -3 = -4.636809248 Reorder the terms: -3 + x = -4.636809248 Solving -3 + x = -4.636809248 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 = -4.636809248 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.636809248 + 3 x = -4.636809248 + 3 Combine like terms: -4.636809248 + 3 = -1.636809248 x = -1.636809248 Simplifying x = -1.636809248Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.636809248, -1.636809248}Solution
x = {7.636809248, -1.636809248}
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