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Simplifying 9(x) = 2.15(2x2 + -4x + -6) Reorder the terms: 9x = 2.15(-6 + -4x + 2x2) 9x = (-6 * 2.15 + -4x * 2.15 + 2x2 * 2.15) 9x = (-12.9 + -8.6x + 4.3x2) Solving 9x = -12.9 + -8.6x + 4.3x2 Solving for variable 'x'. Reorder the terms: 12.9 + 9x + 8.6x + -4.3x2 = -12.9 + -8.6x + 4.3x2 + 12.9 + 8.6x + -4.3x2 Combine like terms: 9x + 8.6x = 17.6x 12.9 + 17.6x + -4.3x2 = -12.9 + -8.6x + 4.3x2 + 12.9 + 8.6x + -4.3x2 Reorder the terms: 12.9 + 17.6x + -4.3x2 = -12.9 + 12.9 + -8.6x + 8.6x + 4.3x2 + -4.3x2 Combine like terms: -12.9 + 12.9 = 0.0 12.9 + 17.6x + -4.3x2 = 0.0 + -8.6x + 8.6x + 4.3x2 + -4.3x2 12.9 + 17.6x + -4.3x2 = -8.6x + 8.6x + 4.3x2 + -4.3x2 Combine like terms: -8.6x + 8.6x = 0.0 12.9 + 17.6x + -4.3x2 = 0.0 + 4.3x2 + -4.3x2 12.9 + 17.6x + -4.3x2 = 4.3x2 + -4.3x2 Combine like terms: 4.3x2 + -4.3x2 = 0.0 12.9 + 17.6x + -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'. -3 + -4.093023256x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -4.093023256x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -4.093023256x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4.093023256x + x2 = 0 + 3 -4.093023256x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -4.093023256x + x2 = 3 The x term is -4.093023256x. Take half its coefficient (-2.046511628). Square it (4.188209844) and add it to both sides. Add '4.188209844' to each side of the equation. -4.093023256x + 4.188209844 + x2 = 3 + 4.188209844 Reorder the terms: 4.188209844 + -4.093023256x + x2 = 3 + 4.188209844 Combine like terms: 3 + 4.188209844 = 7.188209844 4.188209844 + -4.093023256x + x2 = 7.188209844 Factor a perfect square on the left side: (x + -2.046511628)(x + -2.046511628) = 7.188209844 Calculate the square root of the right side: 2.681083707 Break this problem into two subproblems by setting (x + -2.046511628) equal to 2.681083707 and -2.681083707.Subproblem 1
x + -2.046511628 = 2.681083707 Simplifying x + -2.046511628 = 2.681083707 Reorder the terms: -2.046511628 + x = 2.681083707 Solving -2.046511628 + x = 2.681083707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.046511628' to each side of the equation. -2.046511628 + 2.046511628 + x = 2.681083707 + 2.046511628 Combine like terms: -2.046511628 + 2.046511628 = 0.000000000 0.000000000 + x = 2.681083707 + 2.046511628 x = 2.681083707 + 2.046511628 Combine like terms: 2.681083707 + 2.046511628 = 4.727595335 x = 4.727595335 Simplifying x = 4.727595335Subproblem 2
x + -2.046511628 = -2.681083707 Simplifying x + -2.046511628 = -2.681083707 Reorder the terms: -2.046511628 + x = -2.681083707 Solving -2.046511628 + x = -2.681083707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.046511628' to each side of the equation. -2.046511628 + 2.046511628 + x = -2.681083707 + 2.046511628 Combine like terms: -2.046511628 + 2.046511628 = 0.000000000 0.000000000 + x = -2.681083707 + 2.046511628 x = -2.681083707 + 2.046511628 Combine like terms: -2.681083707 + 2.046511628 = -0.634572079 x = -0.634572079 Simplifying x = -0.634572079Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.727595335, -0.634572079}
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