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Simplifying 7 + 3(2x + -9) * x = -1 Reorder the terms: 7 + 3(-9 + 2x) * x = -1 Reorder the terms for easier multiplication: 7 + 3x(-9 + 2x) = -1 7 + (-9 * 3x + 2x * 3x) = -1 7 + (-27x + 6x2) = -1 Solving 7 + -27x + 6x2 = -1 Solving for variable 'x'. Reorder the terms: 7 + 1 + -27x + 6x2 = -1 + 1 Combine like terms: 7 + 1 = 8 8 + -27x + 6x2 = -1 + 1 Combine like terms: -1 + 1 = 0 8 + -27x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.333333333 + -4.5x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -4.5x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -4.5x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -4.5x + x2 = 0 + -1.333333333 -4.5x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -4.5x + x2 = -1.333333333 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -1.333333333 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -1.333333333 + 5.0625 Combine like terms: -1.333333333 + 5.0625 = 3.729166667 5.0625 + -4.5x + x2 = 3.729166667 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 3.729166667 Calculate the square root of the right side: 1.931105038 Break this problem into two subproblems by setting (x + -2.25) equal to 1.931105038 and -1.931105038.Subproblem 1
x + -2.25 = 1.931105038 Simplifying x + -2.25 = 1.931105038 Reorder the terms: -2.25 + x = 1.931105038 Solving -2.25 + x = 1.931105038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 1.931105038 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 1.931105038 + 2.25 x = 1.931105038 + 2.25 Combine like terms: 1.931105038 + 2.25 = 4.181105038 x = 4.181105038 Simplifying x = 4.181105038Subproblem 2
x + -2.25 = -1.931105038 Simplifying x + -2.25 = -1.931105038 Reorder the terms: -2.25 + x = -1.931105038 Solving -2.25 + x = -1.931105038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -1.931105038 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -1.931105038 + 2.25 x = -1.931105038 + 2.25 Combine like terms: -1.931105038 + 2.25 = 0.318894962 x = 0.318894962 Simplifying x = 0.318894962Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.181105038, 0.318894962}
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