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Simplifying 9x2 + 6x + 3x = 72 + -2 + 13x Reorder the terms: 6x + 3x + 9x2 = 72 + -2 + 13x Combine like terms: 6x + 3x = 9x 9x + 9x2 = 72 + -2 + 13x Combine like terms: 72 + -2 = 70 9x + 9x2 = 70 + 13x Solving 9x + 9x2 = 70 + 13x Solving for variable 'x'. Reorder the terms: -70 + 9x + -13x + 9x2 = 70 + 13x + -70 + -13x Combine like terms: 9x + -13x = -4x -70 + -4x + 9x2 = 70 + 13x + -70 + -13x Reorder the terms: -70 + -4x + 9x2 = 70 + -70 + 13x + -13x Combine like terms: 70 + -70 = 0 -70 + -4x + 9x2 = 0 + 13x + -13x -70 + -4x + 9x2 = 13x + -13x Combine like terms: 13x + -13x = 0 -70 + -4x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -7.777777778 + -0.4444444444x + x2 = 0 Move the constant term to the right: Add '7.777777778' to each side of the equation. -7.777777778 + -0.4444444444x + 7.777777778 + x2 = 0 + 7.777777778 Reorder the terms: -7.777777778 + 7.777777778 + -0.4444444444x + x2 = 0 + 7.777777778 Combine like terms: -7.777777778 + 7.777777778 = 0.000000000 0.000000000 + -0.4444444444x + x2 = 0 + 7.777777778 -0.4444444444x + x2 = 0 + 7.777777778 Combine like terms: 0 + 7.777777778 = 7.777777778 -0.4444444444x + x2 = 7.777777778 The x term is -0.4444444444x. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444x + 0.04938271604 + x2 = 7.777777778 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444x + x2 = 7.777777778 + 0.04938271604 Combine like terms: 7.777777778 + 0.04938271604 = 7.82716049404 0.04938271604 + -0.4444444444x + x2 = 7.82716049404 Factor a perfect square on the left side: (x + -0.2222222222)(x + -0.2222222222) = 7.82716049404 Calculate the square root of the right side: 2.797706292 Break this problem into two subproblems by setting (x + -0.2222222222) equal to 2.797706292 and -2.797706292.Subproblem 1
x + -0.2222222222 = 2.797706292 Simplifying x + -0.2222222222 = 2.797706292 Reorder the terms: -0.2222222222 + x = 2.797706292 Solving -0.2222222222 + x = 2.797706292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = 2.797706292 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = 2.797706292 + 0.2222222222 x = 2.797706292 + 0.2222222222 Combine like terms: 2.797706292 + 0.2222222222 = 3.0199285142 x = 3.0199285142 Simplifying x = 3.0199285142Subproblem 2
x + -0.2222222222 = -2.797706292 Simplifying x + -0.2222222222 = -2.797706292 Reorder the terms: -0.2222222222 + x = -2.797706292 Solving -0.2222222222 + x = -2.797706292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = -2.797706292 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = -2.797706292 + 0.2222222222 x = -2.797706292 + 0.2222222222 Combine like terms: -2.797706292 + 0.2222222222 = -2.5754840698 x = -2.5754840698 Simplifying x = -2.5754840698Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.0199285142, -2.5754840698}
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