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Simplifying 9 = 2.15(2x2 + -4x + -6) Reorder the terms: 9 = 2.15(-6 + -4x + 2x2) 9 = (-6 * 2.15 + -4x * 2.15 + 2x2 * 2.15) 9 = (-12.9 + -8.6x + 4.3x2) Solving 9 = -12.9 + -8.6x + 4.3x2 Solving for variable 'x'. Combine like terms: 9 + 12.9 = 21.9 21.9 + 8.6x + -4.3x2 = -12.9 + -8.6x + 4.3x2 + 12.9 + 8.6x + -4.3x2 Reorder the terms: 21.9 + 8.6x + -4.3x2 = -12.9 + 12.9 + -8.6x + 8.6x + 4.3x2 + -4.3x2 Combine like terms: -12.9 + 12.9 = 0.0 21.9 + 8.6x + -4.3x2 = 0.0 + -8.6x + 8.6x + 4.3x2 + -4.3x2 21.9 + 8.6x + -4.3x2 = -8.6x + 8.6x + 4.3x2 + -4.3x2 Combine like terms: -8.6x + 8.6x = 0.0 21.9 + 8.6x + -4.3x2 = 0.0 + 4.3x2 + -4.3x2 21.9 + 8.6x + -4.3x2 = 4.3x2 + -4.3x2 Combine like terms: 4.3x2 + -4.3x2 = 0.0 21.9 + 8.6x + -4.3x2 = 0.0 Begin completing the square. Divide all terms by -4.3 the coefficient of the squared term: Divide each side by '-4.3'. -5.093023256 + -2x + x2 = 0 Move the constant term to the right: Add '5.093023256' to each side of the equation. -5.093023256 + -2x + 5.093023256 + x2 = 0 + 5.093023256 Reorder the terms: -5.093023256 + 5.093023256 + -2x + x2 = 0 + 5.093023256 Combine like terms: -5.093023256 + 5.093023256 = 0.000000000 0.000000000 + -2x + x2 = 0 + 5.093023256 -2x + x2 = 0 + 5.093023256 Combine like terms: 0 + 5.093023256 = 5.093023256 -2x + x2 = 5.093023256 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 5.093023256 + 1 Reorder the terms: 1 + -2x + x2 = 5.093023256 + 1 Combine like terms: 5.093023256 + 1 = 6.093023256 1 + -2x + x2 = 6.093023256 Factor a perfect square on the left side: (x + -1)(x + -1) = 6.093023256 Calculate the square root of the right side: 2.468405002 Break this problem into two subproblems by setting (x + -1) equal to 2.468405002 and -2.468405002.Subproblem 1
x + -1 = 2.468405002 Simplifying x + -1 = 2.468405002 Reorder the terms: -1 + x = 2.468405002 Solving -1 + x = 2.468405002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.468405002 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.468405002 + 1 x = 2.468405002 + 1 Combine like terms: 2.468405002 + 1 = 3.468405002 x = 3.468405002 Simplifying x = 3.468405002Subproblem 2
x + -1 = -2.468405002 Simplifying x + -1 = -2.468405002 Reorder the terms: -1 + x = -2.468405002 Solving -1 + x = -2.468405002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.468405002 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.468405002 + 1 x = -2.468405002 + 1 Combine like terms: -2.468405002 + 1 = -1.468405002 x = -1.468405002 Simplifying x = -1.468405002Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.468405002, -1.468405002}
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