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Simplifying 10x2 + 100x = 1600 Reorder the terms: 100x + 10x2 = 1600 Solving 100x + 10x2 = 1600 Solving for variable 'x'. Reorder the terms: -1600 + 100x + 10x2 = 1600 + -1600 Combine like terms: 1600 + -1600 = 0 -1600 + 100x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-160 + 10x + x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-160 + 10x + x2)' equal to zero and attempt to solve: Simplifying -160 + 10x + x2 = 0 Solving -160 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '160' to each side of the equation. -160 + 10x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + 10x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + 10x + x2 = 0 + 160 10x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 10x + x2 = 160 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 = 160 + 25 Reorder the terms: 25 + 10x + x2 = 160 + 25 Combine like terms: 160 + 25 = 185 25 + 10x + x2 = 185 Factor a perfect square on the left side: (x + 5)(x + 5) = 185 Calculate the square root of the right side: 13.601470509 Break this problem into two subproblems by setting (x + 5) equal to 13.601470509 and -13.601470509.Subproblem 1
x + 5 = 13.601470509 Simplifying x + 5 = 13.601470509 Reorder the terms: 5 + x = 13.601470509 Solving 5 + x = 13.601470509 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 = 13.601470509 + -5 Combine like terms: 5 + -5 = 0 0 + x = 13.601470509 + -5 x = 13.601470509 + -5 Combine like terms: 13.601470509 + -5 = 8.601470509 x = 8.601470509 Simplifying x = 8.601470509Subproblem 2
x + 5 = -13.601470509 Simplifying x + 5 = -13.601470509 Reorder the terms: 5 + x = -13.601470509 Solving 5 + x = -13.601470509 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 = -13.601470509 + -5 Combine like terms: 5 + -5 = 0 0 + x = -13.601470509 + -5 x = -13.601470509 + -5 Combine like terms: -13.601470509 + -5 = -18.601470509 x = -18.601470509 Simplifying x = -18.601470509Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.601470509, -18.601470509}Solution
x = {8.601470509, -18.601470509}
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