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Simplifying 4x2 + -6 = -2x2 + 19x Reorder the terms: -6 + 4x2 = -2x2 + 19x Reorder the terms: -6 + 4x2 = 19x + -2x2 Solving -6 + 4x2 = 19x + -2x2 Solving for variable 'x'. Reorder the terms: -6 + -19x + 4x2 + 2x2 = 19x + -2x2 + -19x + 2x2 Combine like terms: 4x2 + 2x2 = 6x2 -6 + -19x + 6x2 = 19x + -2x2 + -19x + 2x2 Reorder the terms: -6 + -19x + 6x2 = 19x + -19x + -2x2 + 2x2 Combine like terms: 19x + -19x = 0 -6 + -19x + 6x2 = 0 + -2x2 + 2x2 -6 + -19x + 6x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -6 + -19x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1 + -3.166666667x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -3.166666667x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -3.166666667x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3.166666667x + x2 = 0 + 1 -3.166666667x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3.166666667x + x2 = 1 The x term is -3.166666667x. Take half its coefficient (-1.583333334). Square it (2.506944447) and add it to both sides. Add '2.506944447' to each side of the equation. -3.166666667x + 2.506944447 + x2 = 1 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = 1 + 2.506944447 Combine like terms: 1 + 2.506944447 = 3.506944447 2.506944447 + -3.166666667x + x2 = 3.506944447 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 3.506944447 Calculate the square root of the right side: 1.872683755 Break this problem into two subproblems by setting (x + -1.583333334) equal to 1.872683755 and -1.872683755.Subproblem 1
x + -1.583333334 = 1.872683755 Simplifying x + -1.583333334 = 1.872683755 Reorder the terms: -1.583333334 + x = 1.872683755 Solving -1.583333334 + x = 1.872683755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = 1.872683755 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 1.872683755 + 1.583333334 x = 1.872683755 + 1.583333334 Combine like terms: 1.872683755 + 1.583333334 = 3.456017089 x = 3.456017089 Simplifying x = 3.456017089Subproblem 2
x + -1.583333334 = -1.872683755 Simplifying x + -1.583333334 = -1.872683755 Reorder the terms: -1.583333334 + x = -1.872683755 Solving -1.583333334 + x = -1.872683755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = -1.872683755 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -1.872683755 + 1.583333334 x = -1.872683755 + 1.583333334 Combine like terms: -1.872683755 + 1.583333334 = -0.289350421 x = -0.289350421 Simplifying x = -0.289350421Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.456017089, -0.289350421}
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