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Simplifying 3x(3x) + 8x + -11 = 13 + -6x Remove parenthesis around (3x) 3x * 3x + 8x + -11 = 13 + -6x Reorder the terms for easier multiplication: 3 * 3x * x + 8x + -11 = 13 + -6x Multiply 3 * 3 9x * x + 8x + -11 = 13 + -6x Multiply x * x 9x2 + 8x + -11 = 13 + -6x Reorder the terms: -11 + 8x + 9x2 = 13 + -6x Solving -11 + 8x + 9x2 = 13 + -6x Solving for variable 'x'. Reorder the terms: -11 + -13 + 8x + 6x + 9x2 = 13 + -6x + -13 + 6x Combine like terms: -11 + -13 = -24 -24 + 8x + 6x + 9x2 = 13 + -6x + -13 + 6x Combine like terms: 8x + 6x = 14x -24 + 14x + 9x2 = 13 + -6x + -13 + 6x Reorder the terms: -24 + 14x + 9x2 = 13 + -13 + -6x + 6x Combine like terms: 13 + -13 = 0 -24 + 14x + 9x2 = 0 + -6x + 6x -24 + 14x + 9x2 = -6x + 6x Combine like terms: -6x + 6x = 0 -24 + 14x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.666666667 + 1.555555556x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 1.555555556x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 1.555555556x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 1.555555556x + x2 = 0 + 2.666666667 1.555555556x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 1.555555556x + x2 = 2.666666667 The x term is 1.555555556x. Take half its coefficient (0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. 1.555555556x + 0.6049382720 + x2 = 2.666666667 + 0.6049382720 Reorder the terms: 0.6049382720 + 1.555555556x + x2 = 2.666666667 + 0.6049382720 Combine like terms: 2.666666667 + 0.6049382720 = 3.271604939 0.6049382720 + 1.555555556x + x2 = 3.271604939 Factor a perfect square on the left side: (x + 0.777777778)(x + 0.777777778) = 3.271604939 Calculate the square root of the right side: 1.808757844 Break this problem into two subproblems by setting (x + 0.777777778) equal to 1.808757844 and -1.808757844.Subproblem 1
x + 0.777777778 = 1.808757844 Simplifying x + 0.777777778 = 1.808757844 Reorder the terms: 0.777777778 + x = 1.808757844 Solving 0.777777778 + x = 1.808757844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = 1.808757844 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = 1.808757844 + -0.777777778 x = 1.808757844 + -0.777777778 Combine like terms: 1.808757844 + -0.777777778 = 1.030980066 x = 1.030980066 Simplifying x = 1.030980066Subproblem 2
x + 0.777777778 = -1.808757844 Simplifying x + 0.777777778 = -1.808757844 Reorder the terms: 0.777777778 + x = -1.808757844 Solving 0.777777778 + x = -1.808757844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = -1.808757844 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = -1.808757844 + -0.777777778 x = -1.808757844 + -0.777777778 Combine like terms: -1.808757844 + -0.777777778 = -2.586535622 x = -2.586535622 Simplifying x = -2.586535622Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.030980066, -2.586535622}
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