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Simplifying 10000 + 100x = 800 + 10x2 Solving 10000 + 100x = 800 + 10x2 Solving for variable 'x'. Reorder the terms: 10000 + -800 + 100x + -10x2 = 800 + 10x2 + -800 + -10x2 Combine like terms: 10000 + -800 = 9200 9200 + 100x + -10x2 = 800 + 10x2 + -800 + -10x2 Reorder the terms: 9200 + 100x + -10x2 = 800 + -800 + 10x2 + -10x2 Combine like terms: 800 + -800 = 0 9200 + 100x + -10x2 = 0 + 10x2 + -10x2 9200 + 100x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 9200 + 100x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(920 + 10x + -1x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(920 + 10x + -1x2)' equal to zero and attempt to solve: Simplifying 920 + 10x + -1x2 = 0 Solving 920 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -920 + -10x + x2 = 0 Move the constant term to the right: Add '920' to each side of the equation. -920 + -10x + 920 + x2 = 0 + 920 Reorder the terms: -920 + 920 + -10x + x2 = 0 + 920 Combine like terms: -920 + 920 = 0 0 + -10x + x2 = 0 + 920 -10x + x2 = 0 + 920 Combine like terms: 0 + 920 = 920 -10x + x2 = 920 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 = 920 + 25 Reorder the terms: 25 + -10x + x2 = 920 + 25 Combine like terms: 920 + 25 = 945 25 + -10x + x2 = 945 Factor a perfect square on the left side: (x + -5)(x + -5) = 945 Calculate the square root of the right side: 30.740852298 Break this problem into two subproblems by setting (x + -5) equal to 30.740852298 and -30.740852298.Subproblem 1
x + -5 = 30.740852298 Simplifying x + -5 = 30.740852298 Reorder the terms: -5 + x = 30.740852298 Solving -5 + x = 30.740852298 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 = 30.740852298 + 5 Combine like terms: -5 + 5 = 0 0 + x = 30.740852298 + 5 x = 30.740852298 + 5 Combine like terms: 30.740852298 + 5 = 35.740852298 x = 35.740852298 Simplifying x = 35.740852298Subproblem 2
x + -5 = -30.740852298 Simplifying x + -5 = -30.740852298 Reorder the terms: -5 + x = -30.740852298 Solving -5 + x = -30.740852298 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 = -30.740852298 + 5 Combine like terms: -5 + 5 = 0 0 + x = -30.740852298 + 5 x = -30.740852298 + 5 Combine like terms: -30.740852298 + 5 = -25.740852298 x = -25.740852298 Simplifying x = -25.740852298Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.740852298, -25.740852298}Solution
x = {35.740852298, -25.740852298}
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