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Simplifying -16x2 + 160x + 10 = 200 Reorder the terms: 10 + 160x + -16x2 = 200 Solving 10 + 160x + -16x2 = 200 Solving for variable 'x'. Reorder the terms: 10 + -200 + 160x + -16x2 = 200 + -200 Combine like terms: 10 + -200 = -190 -190 + 160x + -16x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -190 + 160x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-95 + 80x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-95 + 80x + -8x2)' equal to zero and attempt to solve: Simplifying -95 + 80x + -8x2 = 0 Solving -95 + 80x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 11.875 + -10x + x2 = 0 Move the constant term to the right: Add '-11.875' to each side of the equation. 11.875 + -10x + -11.875 + x2 = 0 + -11.875 Reorder the terms: 11.875 + -11.875 + -10x + x2 = 0 + -11.875 Combine like terms: 11.875 + -11.875 = 0.000 0.000 + -10x + x2 = 0 + -11.875 -10x + x2 = 0 + -11.875 Combine like terms: 0 + -11.875 = -11.875 -10x + x2 = -11.875 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -11.875 + 25 Reorder the terms: 25 + -10x + x2 = -11.875 + 25 Combine like terms: -11.875 + 25 = 13.125 25 + -10x + x2 = 13.125 Factor a perfect square on the left side: (x + -5)(x + -5) = 13.125 Calculate the square root of the right side: 3.622844187 Break this problem into two subproblems by setting (x + -5) equal to 3.622844187 and -3.622844187.Subproblem 1
x + -5 = 3.622844187 Simplifying x + -5 = 3.622844187 Reorder the terms: -5 + x = 3.622844187 Solving -5 + x = 3.622844187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3.622844187 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.622844187 + 5 x = 3.622844187 + 5 Combine like terms: 3.622844187 + 5 = 8.622844187 x = 8.622844187 Simplifying x = 8.622844187Subproblem 2
x + -5 = -3.622844187 Simplifying x + -5 = -3.622844187 Reorder the terms: -5 + x = -3.622844187 Solving -5 + x = -3.622844187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3.622844187 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.622844187 + 5 x = -3.622844187 + 5 Combine like terms: -3.622844187 + 5 = 1.377155813 x = 1.377155813 Simplifying x = 1.377155813Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.622844187, 1.377155813}Solution
x = {8.622844187, 1.377155813}
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