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Simplifying 10x2 + -20x + -1600 = 0 Reorder the terms: -1600 + -20x + 10x2 = 0 Solving -1600 + -20x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(-160 + -2x + x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-160 + -2x + x2)' equal to zero and attempt to solve: Simplifying -160 + -2x + x2 = 0 Solving -160 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '160' to each side of the equation. -160 + -2x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + -2x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + -2x + x2 = 0 + 160 -2x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 -2x + x2 = 160 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 160 + 1 Reorder the terms: 1 + -2x + x2 = 160 + 1 Combine like terms: 160 + 1 = 161 1 + -2x + x2 = 161 Factor a perfect square on the left side: (x + -1)(x + -1) = 161 Calculate the square root of the right side: 12.68857754 Break this problem into two subproblems by setting (x + -1) equal to 12.68857754 and -12.68857754.Subproblem 1
x + -1 = 12.68857754 Simplifying x + -1 = 12.68857754 Reorder the terms: -1 + x = 12.68857754 Solving -1 + x = 12.68857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 12.68857754 + 1 Combine like terms: -1 + 1 = 0 0 + x = 12.68857754 + 1 x = 12.68857754 + 1 Combine like terms: 12.68857754 + 1 = 13.68857754 x = 13.68857754 Simplifying x = 13.68857754Subproblem 2
x + -1 = -12.68857754 Simplifying x + -1 = -12.68857754 Reorder the terms: -1 + x = -12.68857754 Solving -1 + x = -12.68857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -12.68857754 + 1 Combine like terms: -1 + 1 = 0 0 + x = -12.68857754 + 1 x = -12.68857754 + 1 Combine like terms: -12.68857754 + 1 = -11.68857754 x = -11.68857754 Simplifying x = -11.68857754Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.68857754, -11.68857754}Solution
x = {13.68857754, -11.68857754}
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