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Simplifying 300x2 + -400x + -6 = 0 Reorder the terms: -6 + -400x + 300x2 = 0 Solving -6 + -400x + 300x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -200x + 150x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -200x + 150x2)' equal to zero and attempt to solve: Simplifying -3 + -200x + 150x2 = 0 Solving -3 + -200x + 150x2 = 0 Begin completing the square. Divide all terms by 150 the coefficient of the squared term: Divide each side by '150'. -0.02 + -1.333333333x + x2 = 0.0 Move the constant term to the right: Add '0.02' to each side of the equation. -0.02 + -1.333333333x + 0.02 + x2 = 0.0 + 0.02 Reorder the terms: -0.02 + 0.02 + -1.333333333x + x2 = 0.0 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + -1.333333333x + x2 = 0.0 + 0.02 -1.333333333x + x2 = 0.0 + 0.02 Combine like terms: 0.0 + 0.02 = 0.02 -1.333333333x + x2 = 0.02 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 = 0.02 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 0.02 + 0.4444444442 Combine like terms: 0.02 + 0.4444444442 = 0.4644444442 0.4444444442 + -1.333333333x + x2 = 0.4644444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 0.4644444442 Calculate the square root of the right side: 0.68150161 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 0.68150161 and -0.68150161.Subproblem 1
x + -0.6666666665 = 0.68150161 Simplifying x + -0.6666666665 = 0.68150161 Reorder the terms: -0.6666666665 + x = 0.68150161 Solving -0.6666666665 + x = 0.68150161 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 = 0.68150161 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 0.68150161 + 0.6666666665 x = 0.68150161 + 0.6666666665 Combine like terms: 0.68150161 + 0.6666666665 = 1.3481682765 x = 1.3481682765 Simplifying x = 1.3481682765Subproblem 2
x + -0.6666666665 = -0.68150161 Simplifying x + -0.6666666665 = -0.68150161 Reorder the terms: -0.6666666665 + x = -0.68150161 Solving -0.6666666665 + x = -0.68150161 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 = -0.68150161 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -0.68150161 + 0.6666666665 x = -0.68150161 + 0.6666666665 Combine like terms: -0.68150161 + 0.6666666665 = -0.0148349435 x = -0.0148349435 Simplifying x = -0.0148349435Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3481682765, -0.0148349435}Solution
x = {1.3481682765, -0.0148349435}
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