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Simplifying 15x2 + -20x + 3 = 0 Reorder the terms: 3 + -20x + 15x2 = 0 Solving 3 + -20x + 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 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -1.333333333x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -1.333333333x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -1.333333333x + x2 = 0 + -0.2 -1.333333333x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -1.333333333x + x2 = -0.2 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = -0.2 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -0.2 + 0.4444444442 Combine like terms: -0.2 + 0.4444444442 = 0.2444444442 0.4444444442 + -1.333333333x + x2 = 0.2444444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 0.2444444442 Calculate the square root of the right side: 0.494413232 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 0.494413232 and -0.494413232.Subproblem 1
x + -0.6666666665 = 0.494413232 Simplifying x + -0.6666666665 = 0.494413232 Reorder the terms: -0.6666666665 + x = 0.494413232 Solving -0.6666666665 + x = 0.494413232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 0.494413232 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 0.494413232 + 0.6666666665 x = 0.494413232 + 0.6666666665 Combine like terms: 0.494413232 + 0.6666666665 = 1.1610798985 x = 1.1610798985 Simplifying x = 1.1610798985Subproblem 2
x + -0.6666666665 = -0.494413232 Simplifying x + -0.6666666665 = -0.494413232 Reorder the terms: -0.6666666665 + x = -0.494413232 Solving -0.6666666665 + x = -0.494413232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -0.494413232 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -0.494413232 + 0.6666666665 x = -0.494413232 + 0.6666666665 Combine like terms: -0.494413232 + 0.6666666665 = 0.1722534345 x = 0.1722534345 Simplifying x = 0.1722534345Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1610798985, 0.1722534345}
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