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Simplifying 3x2 + -10x + 6 = 4x + 17 Reorder the terms: 6 + -10x + 3x2 = 4x + 17 Reorder the terms: 6 + -10x + 3x2 = 17 + 4x Solving 6 + -10x + 3x2 = 17 + 4x Solving for variable 'x'. Reorder the terms: 6 + -17 + -10x + -4x + 3x2 = 17 + 4x + -17 + -4x Combine like terms: 6 + -17 = -11 -11 + -10x + -4x + 3x2 = 17 + 4x + -17 + -4x Combine like terms: -10x + -4x = -14x -11 + -14x + 3x2 = 17 + 4x + -17 + -4x Reorder the terms: -11 + -14x + 3x2 = 17 + -17 + 4x + -4x Combine like terms: 17 + -17 = 0 -11 + -14x + 3x2 = 0 + 4x + -4x -11 + -14x + 3x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -11 + -14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.666666667 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + -4.666666667x + 3.666666667 + x2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + -4.666666667x + x2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + -4.666666667x + x2 = 0 + 3.666666667 -4.666666667x + x2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 -4.666666667x + x2 = 3.666666667 The x term is -4.666666667x. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x + 5.444444448 + x2 = 3.666666667 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = 3.666666667 + 5.444444448 Combine like terms: 3.666666667 + 5.444444448 = 9.111111115 5.444444448 + -4.666666667x + x2 = 9.111111115 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 9.111111115 Calculate the square root of the right side: 3.018461713 Break this problem into two subproblems by setting (x + -2.333333334) equal to 3.018461713 and -3.018461713.Subproblem 1
x + -2.333333334 = 3.018461713 Simplifying x + -2.333333334 = 3.018461713 Reorder the terms: -2.333333334 + x = 3.018461713 Solving -2.333333334 + x = 3.018461713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 3.018461713 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 3.018461713 + 2.333333334 x = 3.018461713 + 2.333333334 Combine like terms: 3.018461713 + 2.333333334 = 5.351795047 x = 5.351795047 Simplifying x = 5.351795047Subproblem 2
x + -2.333333334 = -3.018461713 Simplifying x + -2.333333334 = -3.018461713 Reorder the terms: -2.333333334 + x = -3.018461713 Solving -2.333333334 + x = -3.018461713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -3.018461713 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -3.018461713 + 2.333333334 x = -3.018461713 + 2.333333334 Combine like terms: -3.018461713 + 2.333333334 = -0.685128379 x = -0.685128379 Simplifying x = -0.685128379Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.351795047, -0.685128379}
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