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Simplifying 15x2 + -29x + -3 = 0 Reorder the terms: -3 + -29x + 15x2 = 0 Solving -3 + -29x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.2 + -1.933333333x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -1.933333333x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -1.933333333x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -1.933333333x + x2 = 0 + 0.2 -1.933333333x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -1.933333333x + x2 = 0.2 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 = 0.2 + 0.9344444441 Reorder the terms: 0.9344444441 + -1.933333333x + x2 = 0.2 + 0.9344444441 Combine like terms: 0.2 + 0.9344444441 = 1.1344444441 0.9344444441 + -1.933333333x + x2 = 1.1344444441 Factor a perfect square on the left side: (x + -0.9666666665)(x + -0.9666666665) = 1.1344444441 Calculate the square root of the right side: 1.06510302 Break this problem into two subproblems by setting (x + -0.9666666665) equal to 1.06510302 and -1.06510302.Subproblem 1
x + -0.9666666665 = 1.06510302 Simplifying x + -0.9666666665 = 1.06510302 Reorder the terms: -0.9666666665 + x = 1.06510302 Solving -0.9666666665 + x = 1.06510302 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 = 1.06510302 + 0.9666666665 Combine like terms: -0.9666666665 + 0.9666666665 = 0.0000000000 0.0000000000 + x = 1.06510302 + 0.9666666665 x = 1.06510302 + 0.9666666665 Combine like terms: 1.06510302 + 0.9666666665 = 2.0317696865 x = 2.0317696865 Simplifying x = 2.0317696865Subproblem 2
x + -0.9666666665 = -1.06510302 Simplifying x + -0.9666666665 = -1.06510302 Reorder the terms: -0.9666666665 + x = -1.06510302 Solving -0.9666666665 + x = -1.06510302 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 = -1.06510302 + 0.9666666665 Combine like terms: -0.9666666665 + 0.9666666665 = 0.0000000000 0.0000000000 + x = -1.06510302 + 0.9666666665 x = -1.06510302 + 0.9666666665 Combine like terms: -1.06510302 + 0.9666666665 = -0.0984363535 x = -0.0984363535 Simplifying x = -0.0984363535Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0317696865, -0.0984363535}
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