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Simplifying 3(10 + x) + -1(30 + 3x) * x = -4 (10 * 3 + x * 3) + -1(30 + 3x) * x = -4 (30 + 3x) + -1(30 + 3x) * x = -4 Reorder the terms for easier multiplication: 30 + 3x + -1x(30 + 3x) = -4 30 + 3x + (30 * -1x + 3x * -1x) = -4 30 + 3x + (-30x + -3x2) = -4 Combine like terms: 3x + -30x = -27x 30 + -27x + -3x2 = -4 Solving 30 + -27x + -3x2 = -4 Solving for variable 'x'. Reorder the terms: 30 + 4 + -27x + -3x2 = -4 + 4 Combine like terms: 30 + 4 = 34 34 + -27x + -3x2 = -4 + 4 Combine like terms: -4 + 4 = 0 34 + -27x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -11.33333333 + 9x + x2 = 0 Move the constant term to the right: Add '11.33333333' to each side of the equation. -11.33333333 + 9x + 11.33333333 + x2 = 0 + 11.33333333 Reorder the terms: -11.33333333 + 11.33333333 + 9x + x2 = 0 + 11.33333333 Combine like terms: -11.33333333 + 11.33333333 = 0.00000000 0.00000000 + 9x + x2 = 0 + 11.33333333 9x + x2 = 0 + 11.33333333 Combine like terms: 0 + 11.33333333 = 11.33333333 9x + x2 = 11.33333333 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 11.33333333 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 11.33333333 + 20.25 Combine like terms: 11.33333333 + 20.25 = 31.58333333 20.25 + 9x + x2 = 31.58333333 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 31.58333333 Calculate the square root of the right side: 5.6199051 Break this problem into two subproblems by setting (x + 4.5) equal to 5.6199051 and -5.6199051.Subproblem 1
x + 4.5 = 5.6199051 Simplifying x + 4.5 = 5.6199051 Reorder the terms: 4.5 + x = 5.6199051 Solving 4.5 + x = 5.6199051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 5.6199051 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.6199051 + -4.5 x = 5.6199051 + -4.5 Combine like terms: 5.6199051 + -4.5 = 1.1199051 x = 1.1199051 Simplifying x = 1.1199051Subproblem 2
x + 4.5 = -5.6199051 Simplifying x + 4.5 = -5.6199051 Reorder the terms: 4.5 + x = -5.6199051 Solving 4.5 + x = -5.6199051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -5.6199051 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.6199051 + -4.5 x = -5.6199051 + -4.5 Combine like terms: -5.6199051 + -4.5 = -10.1199051 x = -10.1199051 Simplifying x = -10.1199051Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1199051, -10.1199051}
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