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Simplifying 2x(3 + -8x) + (x + 6) = 6x + -3 (3 * 2x + -8x * 2x) + (x + 6) = 6x + -3 (6x + -16x2) + (x + 6) = 6x + -3 Reorder the terms: 6x + -16x2 + (6 + x) = 6x + -3 Remove parenthesis around (6 + x) 6x + -16x2 + 6 + x = 6x + -3 Reorder the terms: 6 + 6x + x + -16x2 = 6x + -3 Combine like terms: 6x + x = 7x 6 + 7x + -16x2 = 6x + -3 Reorder the terms: 6 + 7x + -16x2 = -3 + 6x Solving 6 + 7x + -16x2 = -3 + 6x Solving for variable 'x'. Reorder the terms: 6 + 3 + 7x + -6x + -16x2 = -3 + 6x + 3 + -6x Combine like terms: 6 + 3 = 9 9 + 7x + -6x + -16x2 = -3 + 6x + 3 + -6x Combine like terms: 7x + -6x = 1x 9 + 1x + -16x2 = -3 + 6x + 3 + -6x Reorder the terms: 9 + 1x + -16x2 = -3 + 3 + 6x + -6x Combine like terms: -3 + 3 = 0 9 + 1x + -16x2 = 0 + 6x + -6x 9 + 1x + -16x2 = 6x + -6x Combine like terms: 6x + -6x = 0 9 + 1x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.5625 + -0.0625x + x2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + -0.0625x + 0.5625 + x2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + -0.0625x + x2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + -0.0625x + x2 = 0 + 0.5625 -0.0625x + x2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 -0.0625x + x2 = 0.5625 The x term is -0.0625x. Take half its coefficient (-0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. -0.0625x + 0.0009765625 + x2 = 0.5625 + 0.0009765625 Reorder the terms: 0.0009765625 + -0.0625x + x2 = 0.5625 + 0.0009765625 Combine like terms: 0.5625 + 0.0009765625 = 0.5634765625 0.0009765625 + -0.0625x + x2 = 0.5634765625 Factor a perfect square on the left side: (x + -0.03125)(x + -0.03125) = 0.5634765625 Calculate the square root of the right side: 0.750650759 Break this problem into two subproblems by setting (x + -0.03125) equal to 0.750650759 and -0.750650759.Subproblem 1
x + -0.03125 = 0.750650759 Simplifying x + -0.03125 = 0.750650759 Reorder the terms: -0.03125 + x = 0.750650759 Solving -0.03125 + x = 0.750650759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + x = 0.750650759 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + x = 0.750650759 + 0.03125 x = 0.750650759 + 0.03125 Combine like terms: 0.750650759 + 0.03125 = 0.781900759 x = 0.781900759 Simplifying x = 0.781900759Subproblem 2
x + -0.03125 = -0.750650759 Simplifying x + -0.03125 = -0.750650759 Reorder the terms: -0.03125 + x = -0.750650759 Solving -0.03125 + x = -0.750650759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + x = -0.750650759 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + x = -0.750650759 + 0.03125 x = -0.750650759 + 0.03125 Combine like terms: -0.750650759 + 0.03125 = -0.719400759 x = -0.719400759 Simplifying x = -0.719400759Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.781900759, -0.719400759}
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