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Simplifying 5x(x + 6) = 4(x + 7) Reorder the terms: 5x(6 + x) = 4(x + 7) (6 * 5x + x * 5x) = 4(x + 7) (30x + 5x2) = 4(x + 7) Reorder the terms: 30x + 5x2 = 4(7 + x) 30x + 5x2 = (7 * 4 + x * 4) 30x + 5x2 = (28 + 4x) Solving 30x + 5x2 = 28 + 4x Solving for variable 'x'. Reorder the terms: -28 + 30x + -4x + 5x2 = 28 + 4x + -28 + -4x Combine like terms: 30x + -4x = 26x -28 + 26x + 5x2 = 28 + 4x + -28 + -4x Reorder the terms: -28 + 26x + 5x2 = 28 + -28 + 4x + -4x Combine like terms: 28 + -28 = 0 -28 + 26x + 5x2 = 0 + 4x + -4x -28 + 26x + 5x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -28 + 26x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.6 + 5.2x + x2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + 5.2x + 5.6 + x2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + 5.2x + x2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + 5.2x + x2 = 0 + 5.6 5.2x + x2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 5.2x + x2 = 5.6 The x term is 5.2x. Take half its coefficient (2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. 5.2x + 6.76 + x2 = 5.6 + 6.76 Reorder the terms: 6.76 + 5.2x + x2 = 5.6 + 6.76 Combine like terms: 5.6 + 6.76 = 12.36 6.76 + 5.2x + x2 = 12.36 Factor a perfect square on the left side: (x + 2.6)(x + 2.6) = 12.36 Calculate the square root of the right side: 3.515679166 Break this problem into two subproblems by setting (x + 2.6) equal to 3.515679166 and -3.515679166.Subproblem 1
x + 2.6 = 3.515679166 Simplifying x + 2.6 = 3.515679166 Reorder the terms: 2.6 + x = 3.515679166 Solving 2.6 + x = 3.515679166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = 3.515679166 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = 3.515679166 + -2.6 x = 3.515679166 + -2.6 Combine like terms: 3.515679166 + -2.6 = 0.915679166 x = 0.915679166 Simplifying x = 0.915679166Subproblem 2
x + 2.6 = -3.515679166 Simplifying x + 2.6 = -3.515679166 Reorder the terms: 2.6 + x = -3.515679166 Solving 2.6 + x = -3.515679166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = -3.515679166 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = -3.515679166 + -2.6 x = -3.515679166 + -2.6 Combine like terms: -3.515679166 + -2.6 = -6.115679166 x = -6.115679166 Simplifying x = -6.115679166Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.915679166, -6.115679166}
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