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Simplifying -2x * x + 1700x + 6 = 4x * x + 94x + 3 Multiply x * x -2x2 + 1700x + 6 = 4x * x + 94x + 3 Reorder the terms: 6 + 1700x + -2x2 = 4x * x + 94x + 3 Multiply x * x 6 + 1700x + -2x2 = 4x2 + 94x + 3 Reorder the terms: 6 + 1700x + -2x2 = 3 + 94x + 4x2 Solving 6 + 1700x + -2x2 = 3 + 94x + 4x2 Solving for variable 'x'. Reorder the terms: 6 + -3 + 1700x + -94x + -2x2 + -4x2 = 3 + 94x + 4x2 + -3 + -94x + -4x2 Combine like terms: 6 + -3 = 3 3 + 1700x + -94x + -2x2 + -4x2 = 3 + 94x + 4x2 + -3 + -94x + -4x2 Combine like terms: 1700x + -94x = 1606x 3 + 1606x + -2x2 + -4x2 = 3 + 94x + 4x2 + -3 + -94x + -4x2 Combine like terms: -2x2 + -4x2 = -6x2 3 + 1606x + -6x2 = 3 + 94x + 4x2 + -3 + -94x + -4x2 Reorder the terms: 3 + 1606x + -6x2 = 3 + -3 + 94x + -94x + 4x2 + -4x2 Combine like terms: 3 + -3 = 0 3 + 1606x + -6x2 = 0 + 94x + -94x + 4x2 + -4x2 3 + 1606x + -6x2 = 94x + -94x + 4x2 + -4x2 Combine like terms: 94x + -94x = 0 3 + 1606x + -6x2 = 0 + 4x2 + -4x2 3 + 1606x + -6x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 3 + 1606x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.5 + -267.6666667x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -267.6666667x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -267.6666667x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -267.6666667x + x2 = 0 + 0.5 -267.6666667x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -267.6666667x + x2 = 0.5 The x term is -267.6666667x. Take half its coefficient (-133.8333334). Square it (17911.36113) and add it to both sides. Add '17911.36113' to each side of the equation. -267.6666667x + 17911.36113 + x2 = 0.5 + 17911.36113 Reorder the terms: 17911.36113 + -267.6666667x + x2 = 0.5 + 17911.36113 Combine like terms: 0.5 + 17911.36113 = 17911.86113 17911.36113 + -267.6666667x + x2 = 17911.86113 Factor a perfect square on the left side: (x + -133.8333334)(x + -133.8333334) = 17911.86113 Calculate the square root of the right side: 133.835201386 Break this problem into two subproblems by setting (x + -133.8333334) equal to 133.835201386 and -133.835201386.Subproblem 1
x + -133.8333334 = 133.835201386 Simplifying x + -133.8333334 = 133.835201386 Reorder the terms: -133.8333334 + x = 133.835201386 Solving -133.8333334 + x = 133.835201386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '133.8333334' to each side of the equation. -133.8333334 + 133.8333334 + x = 133.835201386 + 133.8333334 Combine like terms: -133.8333334 + 133.8333334 = 0.0000000 0.0000000 + x = 133.835201386 + 133.8333334 x = 133.835201386 + 133.8333334 Combine like terms: 133.835201386 + 133.8333334 = 267.668534786 x = 267.668534786 Simplifying x = 267.668534786Subproblem 2
x + -133.8333334 = -133.835201386 Simplifying x + -133.8333334 = -133.835201386 Reorder the terms: -133.8333334 + x = -133.835201386 Solving -133.8333334 + x = -133.835201386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '133.8333334' to each side of the equation. -133.8333334 + 133.8333334 + x = -133.835201386 + 133.8333334 Combine like terms: -133.8333334 + 133.8333334 = 0.0000000 0.0000000 + x = -133.835201386 + 133.8333334 x = -133.835201386 + 133.8333334 Combine like terms: -133.835201386 + 133.8333334 = -0.001867986 x = -0.001867986 Simplifying x = -0.001867986Solution
The solution to the problem is based on the solutions from the subproblems. x = {267.668534786, -0.001867986}
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