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Simplifying 3x2 = 7 + -9x Solving 3x2 = 7 + -9x Solving for variable 'x'. Reorder the terms: -7 + 9x + 3x2 = 7 + -9x + -7 + 9x Reorder the terms: -7 + 9x + 3x2 = 7 + -7 + -9x + 9x Combine like terms: 7 + -7 = 0 -7 + 9x + 3x2 = 0 + -9x + 9x -7 + 9x + 3x2 = -9x + 9x Combine like terms: -9x + 9x = 0 -7 + 9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + 3x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 3x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 3x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 3x + x2 = 0 + 2.333333333 3x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 3x + x2 = 2.333333333 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 2.333333333 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 2.333333333 + 2.25 Combine like terms: 2.333333333 + 2.25 = 4.583333333 2.25 + 3x + x2 = 4.583333333 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 4.583333333 Calculate the square root of the right side: 2.140872096 Break this problem into two subproblems by setting (x + 1.5) equal to 2.140872096 and -2.140872096.Subproblem 1
x + 1.5 = 2.140872096 Simplifying x + 1.5 = 2.140872096 Reorder the terms: 1.5 + x = 2.140872096 Solving 1.5 + x = 2.140872096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.140872096 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.140872096 + -1.5 x = 2.140872096 + -1.5 Combine like terms: 2.140872096 + -1.5 = 0.640872096 x = 0.640872096 Simplifying x = 0.640872096Subproblem 2
x + 1.5 = -2.140872096 Simplifying x + 1.5 = -2.140872096 Reorder the terms: 1.5 + x = -2.140872096 Solving 1.5 + x = -2.140872096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.140872096 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.140872096 + -1.5 x = -2.140872096 + -1.5 Combine like terms: -2.140872096 + -1.5 = -3.640872096 x = -3.640872096 Simplifying x = -3.640872096Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.640872096, -3.640872096}
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