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Simplifying 3x(5x + 10) = 12 + x Reorder the terms: 3x(10 + 5x) = 12 + x (10 * 3x + 5x * 3x) = 12 + x (30x + 15x2) = 12 + x Solving 30x + 15x2 = 12 + x Solving for variable 'x'. Reorder the terms: -12 + 30x + -1x + 15x2 = 12 + x + -12 + -1x Combine like terms: 30x + -1x = 29x -12 + 29x + 15x2 = 12 + x + -12 + -1x Reorder the terms: -12 + 29x + 15x2 = 12 + -12 + x + -1x Combine like terms: 12 + -12 = 0 -12 + 29x + 15x2 = 0 + x + -1x -12 + 29x + 15x2 = x + -1x Combine like terms: x + -1x = 0 -12 + 29x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.8 + 1.933333333x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 1.933333333x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 1.933333333x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 1.933333333x + x2 = 0 + 0.8 1.933333333x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 1.933333333x + x2 = 0.8 The x term is 1.933333333x. Take half its coefficient (0.9666666665). Square it (0.9344444441) and add it to both sides. Add '0.9344444441' to each side of the equation. 1.933333333x + 0.9344444441 + x2 = 0.8 + 0.9344444441 Reorder the terms: 0.9344444441 + 1.933333333x + x2 = 0.8 + 0.9344444441 Combine like terms: 0.8 + 0.9344444441 = 1.7344444441 0.9344444441 + 1.933333333x + x2 = 1.7344444441 Factor a perfect square on the left side: (x + 0.9666666665)(x + 0.9666666665) = 1.7344444441 Calculate the square root of the right side: 1.316983084 Break this problem into two subproblems by setting (x + 0.9666666665) equal to 1.316983084 and -1.316983084.Subproblem 1
x + 0.9666666665 = 1.316983084 Simplifying x + 0.9666666665 = 1.316983084 Reorder the terms: 0.9666666665 + x = 1.316983084 Solving 0.9666666665 + x = 1.316983084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9666666665' to each side of the equation. 0.9666666665 + -0.9666666665 + x = 1.316983084 + -0.9666666665 Combine like terms: 0.9666666665 + -0.9666666665 = 0.0000000000 0.0000000000 + x = 1.316983084 + -0.9666666665 x = 1.316983084 + -0.9666666665 Combine like terms: 1.316983084 + -0.9666666665 = 0.3503164175 x = 0.3503164175 Simplifying x = 0.3503164175Subproblem 2
x + 0.9666666665 = -1.316983084 Simplifying x + 0.9666666665 = -1.316983084 Reorder the terms: 0.9666666665 + x = -1.316983084 Solving 0.9666666665 + x = -1.316983084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9666666665' to each side of the equation. 0.9666666665 + -0.9666666665 + x = -1.316983084 + -0.9666666665 Combine like terms: 0.9666666665 + -0.9666666665 = 0.0000000000 0.0000000000 + x = -1.316983084 + -0.9666666665 x = -1.316983084 + -0.9666666665 Combine like terms: -1.316983084 + -0.9666666665 = -2.2836497505 x = -2.2836497505 Simplifying x = -2.2836497505Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3503164175, -2.2836497505}
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