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Simplifying -11x2 + 1430x + -4400 = 0 Reorder the terms: -4400 + 1430x + -11x2 = 0 Solving -4400 + 1430x + -11x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '11'. 11(-400 + 130x + -1x2) = 0 Ignore the factor 11.Subproblem 1
Set the factor '(-400 + 130x + -1x2)' equal to zero and attempt to solve: Simplifying -400 + 130x + -1x2 = 0 Solving -400 + 130x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 400 + -130x + x2 = 0 Move the constant term to the right: Add '-400' to each side of the equation. 400 + -130x + -400 + x2 = 0 + -400 Reorder the terms: 400 + -400 + -130x + x2 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + -130x + x2 = 0 + -400 -130x + x2 = 0 + -400 Combine like terms: 0 + -400 = -400 -130x + x2 = -400 The x term is -130x. Take half its coefficient (-65). Square it (4225) and add it to both sides. Add '4225' to each side of the equation. -130x + 4225 + x2 = -400 + 4225 Reorder the terms: 4225 + -130x + x2 = -400 + 4225 Combine like terms: -400 + 4225 = 3825 4225 + -130x + x2 = 3825 Factor a perfect square on the left side: (x + -65)(x + -65) = 3825 Calculate the square root of the right side: 61.846584384 Break this problem into two subproblems by setting (x + -65) equal to 61.846584384 and -61.846584384.Subproblem 1
x + -65 = 61.846584384 Simplifying x + -65 = 61.846584384 Reorder the terms: -65 + x = 61.846584384 Solving -65 + x = 61.846584384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + x = 61.846584384 + 65 Combine like terms: -65 + 65 = 0 0 + x = 61.846584384 + 65 x = 61.846584384 + 65 Combine like terms: 61.846584384 + 65 = 126.846584384 x = 126.846584384 Simplifying x = 126.846584384Subproblem 2
x + -65 = -61.846584384 Simplifying x + -65 = -61.846584384 Reorder the terms: -65 + x = -61.846584384 Solving -65 + x = -61.846584384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + x = -61.846584384 + 65 Combine like terms: -65 + 65 = 0 0 + x = -61.846584384 + 65 x = -61.846584384 + 65 Combine like terms: -61.846584384 + 65 = 3.153415616 x = 3.153415616 Simplifying x = 3.153415616Solution
The solution to the problem is based on the solutions from the subproblems. x = {126.846584384, 3.153415616}Solution
x = {126.846584384, 3.153415616}
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