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Simplifying 6x2 + 3x + -100 = 0 Reorder the terms: -100 + 3x + 6x2 = 0 Solving -100 + 3x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -16.66666667 + 0.5x + x2 = 0 Move the constant term to the right: Add '16.66666667' to each side of the equation. -16.66666667 + 0.5x + 16.66666667 + x2 = 0 + 16.66666667 Reorder the terms: -16.66666667 + 16.66666667 + 0.5x + x2 = 0 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + 0.5x + x2 = 0 + 16.66666667 0.5x + x2 = 0 + 16.66666667 Combine like terms: 0 + 16.66666667 = 16.66666667 0.5x + x2 = 16.66666667 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 16.66666667 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 16.66666667 + 0.0625 Combine like terms: 16.66666667 + 0.0625 = 16.72916667 0.0625 + 0.5x + x2 = 16.72916667 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 16.72916667 Calculate the square root of the right side: 4.090130398 Break this problem into two subproblems by setting (x + 0.25) equal to 4.090130398 and -4.090130398.Subproblem 1
x + 0.25 = 4.090130398 Simplifying x + 0.25 = 4.090130398 Reorder the terms: 0.25 + x = 4.090130398 Solving 0.25 + x = 4.090130398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 4.090130398 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 4.090130398 + -0.25 x = 4.090130398 + -0.25 Combine like terms: 4.090130398 + -0.25 = 3.840130398 x = 3.840130398 Simplifying x = 3.840130398Subproblem 2
x + 0.25 = -4.090130398 Simplifying x + 0.25 = -4.090130398 Reorder the terms: 0.25 + x = -4.090130398 Solving 0.25 + x = -4.090130398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -4.090130398 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -4.090130398 + -0.25 x = -4.090130398 + -0.25 Combine like terms: -4.090130398 + -0.25 = -4.340130398 x = -4.340130398 Simplifying x = -4.340130398Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.840130398, -4.340130398}
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