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Simplifying -3x(3x + 15) + -1(10 + x) = 35 Reorder the terms: -3x(15 + 3x) + -1(10 + x) = 35 (15 * -3x + 3x * -3x) + -1(10 + x) = 35 (-45x + -9x2) + -1(10 + x) = 35 -45x + -9x2 + (10 * -1 + x * -1) = 35 -45x + -9x2 + (-10 + -1x) = 35 Reorder the terms: -10 + -45x + -1x + -9x2 = 35 Combine like terms: -45x + -1x = -46x -10 + -46x + -9x2 = 35 Solving -10 + -46x + -9x2 = 35 Solving for variable 'x'. Reorder the terms: -10 + -35 + -46x + -9x2 = 35 + -35 Combine like terms: -10 + -35 = -45 -45 + -46x + -9x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -45 + -46x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(45 + 46x + 9x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(45 + 46x + 9x2)' equal to zero and attempt to solve: Simplifying 45 + 46x + 9x2 = 0 Solving 45 + 46x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 5 + 5.111111111x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 5.111111111x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 5.111111111x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 5.111111111x + x2 = 0 + -5 5.111111111x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 5.111111111x + x2 = -5 The x term is 5.111111111x. Take half its coefficient (2.555555556). Square it (6.530864200) and add it to both sides. Add '6.530864200' to each side of the equation. 5.111111111x + 6.530864200 + x2 = -5 + 6.530864200 Reorder the terms: 6.530864200 + 5.111111111x + x2 = -5 + 6.530864200 Combine like terms: -5 + 6.530864200 = 1.5308642 6.530864200 + 5.111111111x + x2 = 1.5308642 Factor a perfect square on the left side: (x + 2.555555556)(x + 2.555555556) = 1.5308642 Calculate the square root of the right side: 1.237280971 Break this problem into two subproblems by setting (x + 2.555555556) equal to 1.237280971 and -1.237280971.Subproblem 1
x + 2.555555556 = 1.237280971 Simplifying x + 2.555555556 = 1.237280971 Reorder the terms: 2.555555556 + x = 1.237280971 Solving 2.555555556 + x = 1.237280971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.555555556' to each side of the equation. 2.555555556 + -2.555555556 + x = 1.237280971 + -2.555555556 Combine like terms: 2.555555556 + -2.555555556 = 0.000000000 0.000000000 + x = 1.237280971 + -2.555555556 x = 1.237280971 + -2.555555556 Combine like terms: 1.237280971 + -2.555555556 = -1.318274585 x = -1.318274585 Simplifying x = -1.318274585Subproblem 2
x + 2.555555556 = -1.237280971 Simplifying x + 2.555555556 = -1.237280971 Reorder the terms: 2.555555556 + x = -1.237280971 Solving 2.555555556 + x = -1.237280971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.555555556' to each side of the equation. 2.555555556 + -2.555555556 + x = -1.237280971 + -2.555555556 Combine like terms: 2.555555556 + -2.555555556 = 0.000000000 0.000000000 + x = -1.237280971 + -2.555555556 x = -1.237280971 + -2.555555556 Combine like terms: -1.237280971 + -2.555555556 = -3.792836527 x = -3.792836527 Simplifying x = -3.792836527Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.318274585, -3.792836527}Solution
x = {-1.318274585, -3.792836527}
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