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Simplifying 1492 = 20x + 4x2 Solving 1492 = 20x + 4x2 Solving for variable 'x'. Reorder the terms: 1492 + -20x + -4x2 = 20x + -20x + 4x2 + -4x2 Combine like terms: 20x + -20x = 0 1492 + -20x + -4x2 = 0 + 4x2 + -4x2 1492 + -20x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 1492 + -20x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(373 + -5x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(373 + -5x + -1x2)' equal to zero and attempt to solve: Simplifying 373 + -5x + -1x2 = 0 Solving 373 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -373 + 5x + x2 = 0 Move the constant term to the right: Add '373' to each side of the equation. -373 + 5x + 373 + x2 = 0 + 373 Reorder the terms: -373 + 373 + 5x + x2 = 0 + 373 Combine like terms: -373 + 373 = 0 0 + 5x + x2 = 0 + 373 5x + x2 = 0 + 373 Combine like terms: 0 + 373 = 373 5x + x2 = 373 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 373 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 373 + 6.25 Combine like terms: 373 + 6.25 = 379.25 6.25 + 5x + x2 = 379.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 379.25 Calculate the square root of the right side: 19.474342094 Break this problem into two subproblems by setting (x + 2.5) equal to 19.474342094 and -19.474342094.Subproblem 1
x + 2.5 = 19.474342094 Simplifying x + 2.5 = 19.474342094 Reorder the terms: 2.5 + x = 19.474342094 Solving 2.5 + x = 19.474342094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 19.474342094 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 19.474342094 + -2.5 x = 19.474342094 + -2.5 Combine like terms: 19.474342094 + -2.5 = 16.974342094 x = 16.974342094 Simplifying x = 16.974342094Subproblem 2
x + 2.5 = -19.474342094 Simplifying x + 2.5 = -19.474342094 Reorder the terms: 2.5 + x = -19.474342094 Solving 2.5 + x = -19.474342094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -19.474342094 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -19.474342094 + -2.5 x = -19.474342094 + -2.5 Combine like terms: -19.474342094 + -2.5 = -21.974342094 x = -21.974342094 Simplifying x = -21.974342094Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.974342094, -21.974342094}Solution
x = {16.974342094, -21.974342094}
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