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Simplifying 100x2 + 100x + -1444 = 0 Reorder the terms: -1444 + 100x + 100x2 = 0 Solving -1444 + 100x + 100x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-361 + 25x + 25x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-361 + 25x + 25x2)' equal to zero and attempt to solve: Simplifying -361 + 25x + 25x2 = 0 Solving -361 + 25x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -14.44 + x + x2 = 0 Move the constant term to the right: Add '14.44' to each side of the equation. -14.44 + x + 14.44 + x2 = 0 + 14.44 Reorder the terms: -14.44 + 14.44 + x + x2 = 0 + 14.44 Combine like terms: -14.44 + 14.44 = 0.00 0.00 + x + x2 = 0 + 14.44 x + x2 = 0 + 14.44 Combine like terms: 0 + 14.44 = 14.44 x + x2 = 14.44 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. + 0.25 + x2 = 14.44 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 14.44 + 0.25 Combine like terms: 14.44 + 0.25 = 14.69 1.25 + x2 = 14.69 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 14.69 Calculate the square root of the right side: 3.832753579 Break this problem into two subproblems by setting (x + 0.5) equal to 3.832753579 and -3.832753579.Subproblem 1
x + 0.5 = 3.832753579 Simplifying x + 0.5 = 3.832753579 Reorder the terms: 0.5 + x = 3.832753579 Solving 0.5 + x = 3.832753579 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 = 3.832753579 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.832753579 + -0.5 x = 3.832753579 + -0.5 Combine like terms: 3.832753579 + -0.5 = 3.332753579 x = 3.332753579 Simplifying x = 3.332753579Subproblem 2
x + 0.5 = -3.832753579 Simplifying x + 0.5 = -3.832753579 Reorder the terms: 0.5 + x = -3.832753579 Solving 0.5 + x = -3.832753579 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 = -3.832753579 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.832753579 + -0.5 x = -3.832753579 + -0.5 Combine like terms: -3.832753579 + -0.5 = -4.332753579 x = -4.332753579 Simplifying x = -4.332753579Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.332753579, -4.332753579}Solution
x = {3.332753579, -4.332753579}
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