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Simplifying 3x(7x + -9) + -19x = -15 Reorder the terms: 3x(-9 + 7x) + -19x = -15 (-9 * 3x + 7x * 3x) + -19x = -15 (-27x + 21x2) + -19x = -15 Reorder the terms: -27x + -19x + 21x2 = -15 Combine like terms: -27x + -19x = -46x -46x + 21x2 = -15 Solving -46x + 21x2 = -15 Solving for variable 'x'. Reorder the terms: 15 + -46x + 21x2 = -15 + 15 Combine like terms: -15 + 15 = 0 15 + -46x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.7142857143 + -2.19047619x + x2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + -2.19047619x + -0.7142857143 + x2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + -2.19047619x + x2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + -2.19047619x + x2 = 0 + -0.7142857143 -2.19047619x + x2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 -2.19047619x + x2 = -0.7142857143 The x term is -2.19047619x. Take half its coefficient (-1.095238095). Square it (1.199546485) and add it to both sides. Add '1.199546485' to each side of the equation. -2.19047619x + 1.199546485 + x2 = -0.7142857143 + 1.199546485 Reorder the terms: 1.199546485 + -2.19047619x + x2 = -0.7142857143 + 1.199546485 Combine like terms: -0.7142857143 + 1.199546485 = 0.4852607707 1.199546485 + -2.19047619x + x2 = 0.4852607707 Factor a perfect square on the left side: (x + -1.095238095)(x + -1.095238095) = 0.4852607707 Calculate the square root of the right side: 0.696606611 Break this problem into two subproblems by setting (x + -1.095238095) equal to 0.696606611 and -0.696606611.Subproblem 1
x + -1.095238095 = 0.696606611 Simplifying x + -1.095238095 = 0.696606611 Reorder the terms: -1.095238095 + x = 0.696606611 Solving -1.095238095 + x = 0.696606611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.095238095' to each side of the equation. -1.095238095 + 1.095238095 + x = 0.696606611 + 1.095238095 Combine like terms: -1.095238095 + 1.095238095 = 0.000000000 0.000000000 + x = 0.696606611 + 1.095238095 x = 0.696606611 + 1.095238095 Combine like terms: 0.696606611 + 1.095238095 = 1.791844706 x = 1.791844706 Simplifying x = 1.791844706Subproblem 2
x + -1.095238095 = -0.696606611 Simplifying x + -1.095238095 = -0.696606611 Reorder the terms: -1.095238095 + x = -0.696606611 Solving -1.095238095 + x = -0.696606611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.095238095' to each side of the equation. -1.095238095 + 1.095238095 + x = -0.696606611 + 1.095238095 Combine like terms: -1.095238095 + 1.095238095 = 0.000000000 0.000000000 + x = -0.696606611 + 1.095238095 x = -0.696606611 + 1.095238095 Combine like terms: -0.696606611 + 1.095238095 = 0.398631484 x = 0.398631484 Simplifying x = 0.398631484Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.791844706, 0.398631484}
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