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Simplifying 3x(2x + 7) = -2 Reorder the terms: 3x(7 + 2x) = -2 (7 * 3x + 2x * 3x) = -2 (21x + 6x2) = -2 Solving 21x + 6x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + 21x + 6x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 21x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.3333333333 + 3.5x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 3.5x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 3.5x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 3.5x + x2 = 0 + -0.3333333333 3.5x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 3.5x + x2 = -0.3333333333 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = -0.3333333333 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = -0.3333333333 + 3.0625 Combine like terms: -0.3333333333 + 3.0625 = 2.7291666667 3.0625 + 3.5x + x2 = 2.7291666667 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 2.7291666667 Calculate the square root of the right side: 1.652018967 Break this problem into two subproblems by setting (x + 1.75) equal to 1.652018967 and -1.652018967.Subproblem 1
x + 1.75 = 1.652018967 Simplifying x + 1.75 = 1.652018967 Reorder the terms: 1.75 + x = 1.652018967 Solving 1.75 + x = 1.652018967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 1.652018967 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 1.652018967 + -1.75 x = 1.652018967 + -1.75 Combine like terms: 1.652018967 + -1.75 = -0.097981033 x = -0.097981033 Simplifying x = -0.097981033Subproblem 2
x + 1.75 = -1.652018967 Simplifying x + 1.75 = -1.652018967 Reorder the terms: 1.75 + x = -1.652018967 Solving 1.75 + x = -1.652018967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -1.652018967 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -1.652018967 + -1.75 x = -1.652018967 + -1.75 Combine like terms: -1.652018967 + -1.75 = -3.402018967 x = -3.402018967 Simplifying x = -3.402018967Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.097981033, -3.402018967}
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