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Simplifying 1750x2 + -196x + -980 = 0 Reorder the terms: -980 + -196x + 1750x2 = 0 Solving -980 + -196x + 1750x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '14'. 14(-70 + -14x + 125x2) = 0 Ignore the factor 14.Subproblem 1
Set the factor '(-70 + -14x + 125x2)' equal to zero and attempt to solve: Simplifying -70 + -14x + 125x2 = 0 Solving -70 + -14x + 125x2 = 0 Begin completing the square. Divide all terms by 125 the coefficient of the squared term: Divide each side by '125'. -0.56 + -0.112x + x2 = 0 Move the constant term to the right: Add '0.56' to each side of the equation. -0.56 + -0.112x + 0.56 + x2 = 0 + 0.56 Reorder the terms: -0.56 + 0.56 + -0.112x + x2 = 0 + 0.56 Combine like terms: -0.56 + 0.56 = 0.00 0.00 + -0.112x + x2 = 0 + 0.56 -0.112x + x2 = 0 + 0.56 Combine like terms: 0 + 0.56 = 0.56 -0.112x + x2 = 0.56 The x term is -0.112x. Take half its coefficient (-0.056). Square it (0.003136) and add it to both sides. Add '0.003136' to each side of the equation. -0.112x + 0.003136 + x2 = 0.56 + 0.003136 Reorder the terms: 0.003136 + -0.112x + x2 = 0.56 + 0.003136 Combine like terms: 0.56 + 0.003136 = 0.563136 0.003136 + -0.112x + x2 = 0.563136 Factor a perfect square on the left side: (x + -0.056)(x + -0.056) = 0.563136 Calculate the square root of the right side: 0.75042388 Break this problem into two subproblems by setting (x + -0.056) equal to 0.75042388 and -0.75042388.Subproblem 1
x + -0.056 = 0.75042388 Simplifying x + -0.056 = 0.75042388 Reorder the terms: -0.056 + x = 0.75042388 Solving -0.056 + x = 0.75042388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.056' to each side of the equation. -0.056 + 0.056 + x = 0.75042388 + 0.056 Combine like terms: -0.056 + 0.056 = 0.000 0.000 + x = 0.75042388 + 0.056 x = 0.75042388 + 0.056 Combine like terms: 0.75042388 + 0.056 = 0.80642388 x = 0.80642388 Simplifying x = 0.80642388Subproblem 2
x + -0.056 = -0.75042388 Simplifying x + -0.056 = -0.75042388 Reorder the terms: -0.056 + x = -0.75042388 Solving -0.056 + x = -0.75042388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.056' to each side of the equation. -0.056 + 0.056 + x = -0.75042388 + 0.056 Combine like terms: -0.056 + 0.056 = 0.000 0.000 + x = -0.75042388 + 0.056 x = -0.75042388 + 0.056 Combine like terms: -0.75042388 + 0.056 = -0.69442388 x = -0.69442388 Simplifying x = -0.69442388Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.80642388, -0.69442388}Solution
x = {0.80642388, -0.69442388}
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