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Simplifying 400 = -16x2 + 160x + 1200 Reorder the terms: 400 = 1200 + 160x + -16x2 Solving 400 = 1200 + 160x + -16x2 Solving for variable 'x'. Combine like terms: 400 + -1200 = -800 -800 + -160x + 16x2 = 1200 + 160x + -16x2 + -1200 + -160x + 16x2 Reorder the terms: -800 + -160x + 16x2 = 1200 + -1200 + 160x + -160x + -16x2 + 16x2 Combine like terms: 1200 + -1200 = 0 -800 + -160x + 16x2 = 0 + 160x + -160x + -16x2 + 16x2 -800 + -160x + 16x2 = 160x + -160x + -16x2 + 16x2 Combine like terms: 160x + -160x = 0 -800 + -160x + 16x2 = 0 + -16x2 + 16x2 -800 + -160x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -800 + -160x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-50 + -10x + x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-50 + -10x + x2)' equal to zero and attempt to solve: Simplifying -50 + -10x + x2 = 0 Solving -50 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -10x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -10x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -10x + x2 = 0 + 50 -10x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -10x + x2 = 50 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 = 50 + 25 Reorder the terms: 25 + -10x + x2 = 50 + 25 Combine like terms: 50 + 25 = 75 25 + -10x + x2 = 75 Factor a perfect square on the left side: (x + -5)(x + -5) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x + -5) equal to 8.660254038 and -8.660254038.Subproblem 1
x + -5 = 8.660254038 Simplifying x + -5 = 8.660254038 Reorder the terms: -5 + x = 8.660254038 Solving -5 + x = 8.660254038 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 = 8.660254038 + 5 Combine like terms: -5 + 5 = 0 0 + x = 8.660254038 + 5 x = 8.660254038 + 5 Combine like terms: 8.660254038 + 5 = 13.660254038 x = 13.660254038 Simplifying x = 13.660254038Subproblem 2
x + -5 = -8.660254038 Simplifying x + -5 = -8.660254038 Reorder the terms: -5 + x = -8.660254038 Solving -5 + x = -8.660254038 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 = -8.660254038 + 5 Combine like terms: -5 + 5 = 0 0 + x = -8.660254038 + 5 x = -8.660254038 + 5 Combine like terms: -8.660254038 + 5 = -3.660254038 x = -3.660254038 Simplifying x = -3.660254038Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.660254038, -3.660254038}Solution
x = {13.660254038, -3.660254038}
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