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Simplifying 15x2 + -1x + -6 = 236 Reorder the terms: -6 + -1x + 15x2 = 236 Solving -6 + -1x + 15x2 = 236 Solving for variable 'x'. Reorder the terms: -6 + -236 + -1x + 15x2 = 236 + -236 Combine like terms: -6 + -236 = -242 -242 + -1x + 15x2 = 236 + -236 Combine like terms: 236 + -236 = 0 -242 + -1x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -16.13333333 + -0.06666666667x + x2 = 0 Move the constant term to the right: Add '16.13333333' to each side of the equation. -16.13333333 + -0.06666666667x + 16.13333333 + x2 = 0 + 16.13333333 Reorder the terms: -16.13333333 + 16.13333333 + -0.06666666667x + x2 = 0 + 16.13333333 Combine like terms: -16.13333333 + 16.13333333 = 0.00000000 0.00000000 + -0.06666666667x + x2 = 0 + 16.13333333 -0.06666666667x + x2 = 0 + 16.13333333 Combine like terms: 0 + 16.13333333 = 16.13333333 -0.06666666667x + x2 = 16.13333333 The x term is -0.06666666667x. Take half its coefficient (-0.03333333334). Square it (0.001111111112) and add it to both sides. Add '0.001111111112' to each side of the equation. -0.06666666667x + 0.001111111112 + x2 = 16.13333333 + 0.001111111112 Reorder the terms: 0.001111111112 + -0.06666666667x + x2 = 16.13333333 + 0.001111111112 Combine like terms: 16.13333333 + 0.001111111112 = 16.134444441112 0.001111111112 + -0.06666666667x + x2 = 16.134444441112 Factor a perfect square on the left side: (x + -0.03333333334)(x + -0.03333333334) = 16.134444441112 Calculate the square root of the right side: 4.016770399 Break this problem into two subproblems by setting (x + -0.03333333334) equal to 4.016770399 and -4.016770399.Subproblem 1
x + -0.03333333334 = 4.016770399 Simplifying x + -0.03333333334 = 4.016770399 Reorder the terms: -0.03333333334 + x = 4.016770399 Solving -0.03333333334 + x = 4.016770399 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03333333334' to each side of the equation. -0.03333333334 + 0.03333333334 + x = 4.016770399 + 0.03333333334 Combine like terms: -0.03333333334 + 0.03333333334 = 0.00000000000 0.00000000000 + x = 4.016770399 + 0.03333333334 x = 4.016770399 + 0.03333333334 Combine like terms: 4.016770399 + 0.03333333334 = 4.05010373234 x = 4.05010373234 Simplifying x = 4.05010373234Subproblem 2
x + -0.03333333334 = -4.016770399 Simplifying x + -0.03333333334 = -4.016770399 Reorder the terms: -0.03333333334 + x = -4.016770399 Solving -0.03333333334 + x = -4.016770399 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03333333334' to each side of the equation. -0.03333333334 + 0.03333333334 + x = -4.016770399 + 0.03333333334 Combine like terms: -0.03333333334 + 0.03333333334 = 0.00000000000 0.00000000000 + x = -4.016770399 + 0.03333333334 x = -4.016770399 + 0.03333333334 Combine like terms: -4.016770399 + 0.03333333334 = -3.98343706566 x = -3.98343706566 Simplifying x = -3.98343706566Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.05010373234, -3.98343706566}
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