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Simplifying (5) * 3x2 + 2x + 3 = 6(5) Multiply 5 * 3 15x2 + 2x + 3 = 6(5) Reorder the terms: 3 + 2x + 15x2 = 6(5) Multiply 6 * 5 3 + 2x + 15x2 = 30 Solving 3 + 2x + 15x2 = 30 Solving for variable 'x'. Reorder the terms: 3 + -30 + 2x + 15x2 = 30 + -30 Combine like terms: 3 + -30 = -27 -27 + 2x + 15x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -27 + 2x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -1.8 + 0.1333333333x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 0.1333333333x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 0.1333333333x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 0.1333333333x + x2 = 0 + 1.8 0.1333333333x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 0.1333333333x + x2 = 1.8 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 = 1.8 + 0.004444444442 Reorder the terms: 0.004444444442 + 0.1333333333x + x2 = 1.8 + 0.004444444442 Combine like terms: 1.8 + 0.004444444442 = 1.804444444442 0.004444444442 + 0.1333333333x + x2 = 1.804444444442 Factor a perfect square on the left side: (x + 0.06666666665)(x + 0.06666666665) = 1.804444444442 Calculate the square root of the right side: 1.343296112 Break this problem into two subproblems by setting (x + 0.06666666665) equal to 1.343296112 and -1.343296112.Subproblem 1
x + 0.06666666665 = 1.343296112 Simplifying x + 0.06666666665 = 1.343296112 Reorder the terms: 0.06666666665 + x = 1.343296112 Solving 0.06666666665 + x = 1.343296112 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 = 1.343296112 + -0.06666666665 Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000 0.00000000000 + x = 1.343296112 + -0.06666666665 x = 1.343296112 + -0.06666666665 Combine like terms: 1.343296112 + -0.06666666665 = 1.27662944535 x = 1.27662944535 Simplifying x = 1.27662944535Subproblem 2
x + 0.06666666665 = -1.343296112 Simplifying x + 0.06666666665 = -1.343296112 Reorder the terms: 0.06666666665 + x = -1.343296112 Solving 0.06666666665 + x = -1.343296112 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 = -1.343296112 + -0.06666666665 Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000 0.00000000000 + x = -1.343296112 + -0.06666666665 x = -1.343296112 + -0.06666666665 Combine like terms: -1.343296112 + -0.06666666665 = -1.40996277865 x = -1.40996277865 Simplifying x = -1.40996277865Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.27662944535, -1.40996277865}
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