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Simplifying 3x(5 + -7x) + -2(x + -8) = 0 (5 * 3x + -7x * 3x) + -2(x + -8) = 0 (15x + -21x2) + -2(x + -8) = 0 Reorder the terms: 15x + -21x2 + -2(-8 + x) = 0 15x + -21x2 + (-8 * -2 + x * -2) = 0 15x + -21x2 + (16 + -2x) = 0 Reorder the terms: 16 + 15x + -2x + -21x2 = 0 Combine like terms: 15x + -2x = 13x 16 + 13x + -21x2 = 0 Solving 16 + 13x + -21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -21 the coefficient of the squared term: Divide each side by '-21'. -0.7619047619 + -0.619047619x + x2 = 0 Move the constant term to the right: Add '0.7619047619' to each side of the equation. -0.7619047619 + -0.619047619x + 0.7619047619 + x2 = 0 + 0.7619047619 Reorder the terms: -0.7619047619 + 0.7619047619 + -0.619047619x + x2 = 0 + 0.7619047619 Combine like terms: -0.7619047619 + 0.7619047619 = 0.0000000000 0.0000000000 + -0.619047619x + x2 = 0 + 0.7619047619 -0.619047619x + x2 = 0 + 0.7619047619 Combine like terms: 0 + 0.7619047619 = 0.7619047619 -0.619047619x + x2 = 0.7619047619 The x term is -0.619047619x. Take half its coefficient (-0.3095238095). Square it (0.09580498865) and add it to both sides. Add '0.09580498865' to each side of the equation. -0.619047619x + 0.09580498865 + x2 = 0.7619047619 + 0.09580498865 Reorder the terms: 0.09580498865 + -0.619047619x + x2 = 0.7619047619 + 0.09580498865 Combine like terms: 0.7619047619 + 0.09580498865 = 0.85770975055 0.09580498865 + -0.619047619x + x2 = 0.85770975055 Factor a perfect square on the left side: (x + -0.3095238095)(x + -0.3095238095) = 0.85770975055 Calculate the square root of the right side: 0.926126207 Break this problem into two subproblems by setting (x + -0.3095238095) equal to 0.926126207 and -0.926126207.Subproblem 1
x + -0.3095238095 = 0.926126207 Simplifying x + -0.3095238095 = 0.926126207 Reorder the terms: -0.3095238095 + x = 0.926126207 Solving -0.3095238095 + x = 0.926126207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3095238095' to each side of the equation. -0.3095238095 + 0.3095238095 + x = 0.926126207 + 0.3095238095 Combine like terms: -0.3095238095 + 0.3095238095 = 0.0000000000 0.0000000000 + x = 0.926126207 + 0.3095238095 x = 0.926126207 + 0.3095238095 Combine like terms: 0.926126207 + 0.3095238095 = 1.2356500165 x = 1.2356500165 Simplifying x = 1.2356500165Subproblem 2
x + -0.3095238095 = -0.926126207 Simplifying x + -0.3095238095 = -0.926126207 Reorder the terms: -0.3095238095 + x = -0.926126207 Solving -0.3095238095 + x = -0.926126207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3095238095' to each side of the equation. -0.3095238095 + 0.3095238095 + x = -0.926126207 + 0.3095238095 Combine like terms: -0.3095238095 + 0.3095238095 = 0.0000000000 0.0000000000 + x = -0.926126207 + 0.3095238095 x = -0.926126207 + 0.3095238095 Combine like terms: -0.926126207 + 0.3095238095 = -0.6166023975 x = -0.6166023975 Simplifying x = -0.6166023975Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2356500165, -0.6166023975}
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