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Simplifying 200 = 144x + -16x2 Solving 200 = 144x + -16x2 Solving for variable 'x'. Reorder the terms: 200 + -144x + 16x2 = 144x + -144x + -16x2 + 16x2 Combine like terms: 144x + -144x = 0 200 + -144x + 16x2 = 0 + -16x2 + 16x2 200 + -144x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 200 + -144x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(25 + -18x + 2x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(25 + -18x + 2x2)' equal to zero and attempt to solve: Simplifying 25 + -18x + 2x2 = 0 Solving 25 + -18x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12.5 + -9x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -9x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -9x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -9x + x2 = 0 + -12.5 -9x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -9x + x2 = -12.5 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -12.5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -12.5 + 20.25 Combine like terms: -12.5 + 20.25 = 7.75 20.25 + -9x + x2 = 7.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (x + -4.5) equal to 2.783882181 and -2.783882181.Subproblem 1
x + -4.5 = 2.783882181 Simplifying x + -4.5 = 2.783882181 Reorder the terms: -4.5 + x = 2.783882181 Solving -4.5 + x = 2.783882181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 2.783882181 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 2.783882181 + 4.5 x = 2.783882181 + 4.5 Combine like terms: 2.783882181 + 4.5 = 7.283882181 x = 7.283882181 Simplifying x = 7.283882181Subproblem 2
x + -4.5 = -2.783882181 Simplifying x + -4.5 = -2.783882181 Reorder the terms: -4.5 + x = -2.783882181 Solving -4.5 + x = -2.783882181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -2.783882181 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -2.783882181 + 4.5 x = -2.783882181 + 4.5 Combine like terms: -2.783882181 + 4.5 = 1.716117819 x = 1.716117819 Simplifying x = 1.716117819Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.283882181, 1.716117819}Solution
x = {7.283882181, 1.716117819}
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