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Simplifying 100x2 + 10x = 40 Reorder the terms: 10x + 100x2 = 40 Solving 10x + 100x2 = 40 Solving for variable 'x'. Reorder the terms: -40 + 10x + 100x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + 10x + 100x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-4 + x + 10x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-4 + x + 10x2)' equal to zero and attempt to solve: Simplifying -4 + x + 10x2 = 0 Solving -4 + x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.4 + 0.1x + x2 = 0.0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 0.1x + 0.4 + x2 = 0.0 + 0.4 Reorder the terms: -0.4 + 0.4 + 0.1x + x2 = 0.0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.1x + x2 = 0.0 + 0.4 0.1x + x2 = 0.0 + 0.4 Combine like terms: 0.0 + 0.4 = 0.4 0.1x + x2 = 0.4 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1x + 0.25 + x2 = 0.4 + 0.25 Reorder the terms: 0.25 + 0.1x + x2 = 0.4 + 0.25 Combine like terms: 0.4 + 0.25 = 0.65 0.25 + 0.1x + x2 = 0.65 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.65 Calculate the square root of the right side: 0.806225775 Break this problem into two subproblems by setting (x + 0.5) equal to 0.806225775 and -0.806225775.Subproblem 1
x + 0.5 = 0.806225775 Simplifying x + 0.5 = 0.806225775 Reorder the terms: 0.5 + x = 0.806225775 Solving 0.5 + x = 0.806225775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.806225775 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.806225775 + -0.5 x = 0.806225775 + -0.5 Combine like terms: 0.806225775 + -0.5 = 0.306225775 x = 0.306225775 Simplifying x = 0.306225775Subproblem 2
x + 0.5 = -0.806225775 Simplifying x + 0.5 = -0.806225775 Reorder the terms: 0.5 + x = -0.806225775 Solving 0.5 + x = -0.806225775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.806225775 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.806225775 + -0.5 x = -0.806225775 + -0.5 Combine like terms: -0.806225775 + -0.5 = -1.306225775 x = -1.306225775 Simplifying x = -1.306225775Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.306225775, -1.306225775}Solution
x = {0.306225775, -1.306225775}
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