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Simplifying 200 = 16x2 + 216x Reorder the terms: 200 = 216x + 16x2 Solving 200 = 216x + 16x2 Solving for variable 'x'. Reorder the terms: 200 + -216x + -16x2 = 216x + -216x + 16x2 + -16x2 Combine like terms: 216x + -216x = 0 200 + -216x + -16x2 = 0 + 16x2 + -16x2 200 + -216x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 200 + -216x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(25 + -27x + -2x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(25 + -27x + -2x2)' equal to zero and attempt to solve: Simplifying 25 + -27x + -2x2 = 0 Solving 25 + -27x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -12.5 + 13.5x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 13.5x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 13.5x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 13.5x + x2 = 0 + 12.5 13.5x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 13.5x + x2 = 12.5 The x term is 13.5x. Take half its coefficient (6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. 13.5x + 45.5625 + x2 = 12.5 + 45.5625 Reorder the terms: 45.5625 + 13.5x + x2 = 12.5 + 45.5625 Combine like terms: 12.5 + 45.5625 = 58.0625 45.5625 + 13.5x + x2 = 58.0625 Factor a perfect square on the left side: (x + 6.75)(x + 6.75) = 58.0625 Calculate the square root of the right side: 7.619875327 Break this problem into two subproblems by setting (x + 6.75) equal to 7.619875327 and -7.619875327.Subproblem 1
x + 6.75 = 7.619875327 Simplifying x + 6.75 = 7.619875327 Reorder the terms: 6.75 + x = 7.619875327 Solving 6.75 + x = 7.619875327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + x = 7.619875327 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = 7.619875327 + -6.75 x = 7.619875327 + -6.75 Combine like terms: 7.619875327 + -6.75 = 0.869875327 x = 0.869875327 Simplifying x = 0.869875327Subproblem 2
x + 6.75 = -7.619875327 Simplifying x + 6.75 = -7.619875327 Reorder the terms: 6.75 + x = -7.619875327 Solving 6.75 + x = -7.619875327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + x = -7.619875327 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = -7.619875327 + -6.75 x = -7.619875327 + -6.75 Combine like terms: -7.619875327 + -6.75 = -14.369875327 x = -14.369875327 Simplifying x = -14.369875327Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.869875327, -14.369875327}Solution
x = {0.869875327, -14.369875327}
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