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Simplifying 15x2 = 2x + 3 Reorder the terms: 15x2 = 3 + 2x Solving 15x2 = 3 + 2x Solving for variable 'x'. Reorder the terms: -3 + -2x + 15x2 = 3 + 2x + -3 + -2x Reorder the terms: -3 + -2x + 15x2 = 3 + -3 + 2x + -2x Combine like terms: 3 + -3 = 0 -3 + -2x + 15x2 = 0 + 2x + -2x -3 + -2x + 15x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -3 + -2x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.2 + -0.1333333333x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.1333333333x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.1333333333x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.1333333333x + x2 = 0 + 0.2 -0.1333333333x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.1333333333x + x2 = 0.2 The x term is -0.1333333333x. Take half its coefficient (-0.06666666665). Square it (0.004444444442) and add it to both sides. Add '0.004444444442' to each side of the equation. -0.1333333333x + 0.004444444442 + x2 = 0.2 + 0.004444444442 Reorder the terms: 0.004444444442 + -0.1333333333x + x2 = 0.2 + 0.004444444442 Combine like terms: 0.2 + 0.004444444442 = 0.204444444442 0.004444444442 + -0.1333333333x + x2 = 0.204444444442 Factor a perfect square on the left side: (x + -0.06666666665)(x + -0.06666666665) = 0.204444444442 Calculate the square root of the right side: 0.452155332 Break this problem into two subproblems by setting (x + -0.06666666665) equal to 0.452155332 and -0.452155332.Subproblem 1
x + -0.06666666665 = 0.452155332 Simplifying x + -0.06666666665 = 0.452155332 Reorder the terms: -0.06666666665 + x = 0.452155332 Solving -0.06666666665 + x = 0.452155332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06666666665' to each side of the equation. -0.06666666665 + 0.06666666665 + x = 0.452155332 + 0.06666666665 Combine like terms: -0.06666666665 + 0.06666666665 = 0.00000000000 0.00000000000 + x = 0.452155332 + 0.06666666665 x = 0.452155332 + 0.06666666665 Combine like terms: 0.452155332 + 0.06666666665 = 0.51882199865 x = 0.51882199865 Simplifying x = 0.51882199865Subproblem 2
x + -0.06666666665 = -0.452155332 Simplifying x + -0.06666666665 = -0.452155332 Reorder the terms: -0.06666666665 + x = -0.452155332 Solving -0.06666666665 + x = -0.452155332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06666666665' to each side of the equation. -0.06666666665 + 0.06666666665 + x = -0.452155332 + 0.06666666665 Combine like terms: -0.06666666665 + 0.06666666665 = 0.00000000000 0.00000000000 + x = -0.452155332 + 0.06666666665 x = -0.452155332 + 0.06666666665 Combine like terms: -0.452155332 + 0.06666666665 = -0.38548866535 x = -0.38548866535 Simplifying x = -0.38548866535Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.51882199865, -0.38548866535}
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