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Simplifying 0 = 4x2 + -76x + -133 Reorder the terms: 0 = -133 + -76x + 4x2 Solving 0 = -133 + -76x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 133 = 133 133 + 76x + -4x2 = -133 + -76x + 4x2 + 133 + 76x + -4x2 Reorder the terms: 133 + 76x + -4x2 = -133 + 133 + -76x + 76x + 4x2 + -4x2 Combine like terms: -133 + 133 = 0 133 + 76x + -4x2 = 0 + -76x + 76x + 4x2 + -4x2 133 + 76x + -4x2 = -76x + 76x + 4x2 + -4x2 Combine like terms: -76x + 76x = 0 133 + 76x + -4x2 = 0 + 4x2 + -4x2 133 + 76x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 133 + 76x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -33.25 + -19x + x2 = 0 Move the constant term to the right: Add '33.25' to each side of the equation. -33.25 + -19x + 33.25 + x2 = 0 + 33.25 Reorder the terms: -33.25 + 33.25 + -19x + x2 = 0 + 33.25 Combine like terms: -33.25 + 33.25 = 0.00 0.00 + -19x + x2 = 0 + 33.25 -19x + x2 = 0 + 33.25 Combine like terms: 0 + 33.25 = 33.25 -19x + x2 = 33.25 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 33.25 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 33.25 + 90.25 Combine like terms: 33.25 + 90.25 = 123.5 90.25 + -19x + x2 = 123.5 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 123.5 Calculate the square root of the right side: 11.113055385 Break this problem into two subproblems by setting (x + -9.5) equal to 11.113055385 and -11.113055385.Subproblem 1
x + -9.5 = 11.113055385 Simplifying x + -9.5 = 11.113055385 Reorder the terms: -9.5 + x = 11.113055385 Solving -9.5 + x = 11.113055385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 11.113055385 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 11.113055385 + 9.5 x = 11.113055385 + 9.5 Combine like terms: 11.113055385 + 9.5 = 20.613055385 x = 20.613055385 Simplifying x = 20.613055385Subproblem 2
x + -9.5 = -11.113055385 Simplifying x + -9.5 = -11.113055385 Reorder the terms: -9.5 + x = -11.113055385 Solving -9.5 + x = -11.113055385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -11.113055385 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -11.113055385 + 9.5 x = -11.113055385 + 9.5 Combine like terms: -11.113055385 + 9.5 = -1.613055385 x = -1.613055385 Simplifying x = -1.613055385Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.613055385, -1.613055385}
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