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Simplifying 6x(x + 3) + x = 7x + 5 Reorder the terms: 6x(3 + x) + x = 7x + 5 (3 * 6x + x * 6x) + x = 7x + 5 (18x + 6x2) + x = 7x + 5 Reorder the terms: 18x + x + 6x2 = 7x + 5 Combine like terms: 18x + x = 19x 19x + 6x2 = 7x + 5 Reorder the terms: 19x + 6x2 = 5 + 7x Solving 19x + 6x2 = 5 + 7x Solving for variable 'x'. Reorder the terms: -5 + 19x + -7x + 6x2 = 5 + 7x + -5 + -7x Combine like terms: 19x + -7x = 12x -5 + 12x + 6x2 = 5 + 7x + -5 + -7x Reorder the terms: -5 + 12x + 6x2 = 5 + -5 + 7x + -7x Combine like terms: 5 + -5 = 0 -5 + 12x + 6x2 = 0 + 7x + -7x -5 + 12x + 6x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -5 + 12x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + 2x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + 2x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + 2x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + 0.8333333333 2x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 2x + x2 = 0.8333333333 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.8333333333 + 1 Reorder the terms: 1 + 2x + x2 = 0.8333333333 + 1 Combine like terms: 0.8333333333 + 1 = 1.8333333333 1 + 2x + x2 = 1.8333333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.8333333333 Calculate the square root of the right side: 1.354006401 Break this problem into two subproblems by setting (x + 1) equal to 1.354006401 and -1.354006401.Subproblem 1
x + 1 = 1.354006401 Simplifying x + 1 = 1.354006401 Reorder the terms: 1 + x = 1.354006401 Solving 1 + x = 1.354006401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.354006401 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.354006401 + -1 x = 1.354006401 + -1 Combine like terms: 1.354006401 + -1 = 0.354006401 x = 0.354006401 Simplifying x = 0.354006401Subproblem 2
x + 1 = -1.354006401 Simplifying x + 1 = -1.354006401 Reorder the terms: 1 + x = -1.354006401 Solving 1 + x = -1.354006401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.354006401 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.354006401 + -1 x = -1.354006401 + -1 Combine like terms: -1.354006401 + -1 = -2.354006401 x = -2.354006401 Simplifying x = -2.354006401Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.354006401, -2.354006401}
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