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Simplifying 7x + 4 + 7x + 4 + 7x + 4 + 7x + 4 + 5(x + -2) * 5(x + -2) = 720 Reorder the terms: 7x + 4 + 7x + 4 + 7x + 4 + 7x + 4 + 5(-2 + x) * 5(x + -2) = 720 Reorder the terms: 7x + 4 + 7x + 4 + 7x + 4 + 7x + 4 + 5(-2 + x) * 5(-2 + x) = 720 Reorder the terms for easier multiplication: 7x + 4 + 7x + 4 + 7x + 4 + 7x + 4 + 5 * 5(-2 + x)(-2 + x) = 720 Multiply 5 * 5 7x + 4 + 7x + 4 + 7x + 4 + 7x + 4 + 25(-2 + x)(-2 + x) = 720 Multiply (-2 + x) * (-2 + x) 7x + 4 + 7x + 4 + 7x + 4 + 7x + 4 + 25(-2(-2 + x) + x(-2 + x)) = 720 7x + 4 + 7x + 4 + 7x + 4 + 7x + 4 + 25((-2 * -2 + x * -2) + x(-2 + x)) = 720 7x + 4 + 7x + 4 + 7x + 4 + 7x + 4 + 25((4 + -2x) + x(-2 + x)) = 720 7x + 4 + 7x + 4 + 7x + 4 + 7x + 4 + 25(4 + -2x + (-2 * x + x * x)) = 720 7x + 4 + 7x + 4 + 7x + 4 + 7x + 4 + 25(4 + -2x + (-2x + x2)) = 720 Combine like terms: -2x + -2x = -4x 7x + 4 + 7x + 4 + 7x + 4 + 7x + 4 + 25(4 + -4x + x2) = 720 7x + 4 + 7x + 4 + 7x + 4 + 7x + 4 + (4 * 25 + -4x * 25 + x2 * 25) = 720 7x + 4 + 7x + 4 + 7x + 4 + 7x + 4 + (100 + -100x + 25x2) = 720 Reorder the terms: 4 + 4 + 4 + 4 + 100 + 7x + 7x + 7x + 7x + -100x + 25x2 = 720 Combine like terms: 4 + 4 = 8 8 + 4 + 4 + 100 + 7x + 7x + 7x + 7x + -100x + 25x2 = 720 Combine like terms: 8 + 4 = 12 12 + 4 + 100 + 7x + 7x + 7x + 7x + -100x + 25x2 = 720 Combine like terms: 12 + 4 = 16 16 + 100 + 7x + 7x + 7x + 7x + -100x + 25x2 = 720 Combine like terms: 16 + 100 = 116 116 + 7x + 7x + 7x + 7x + -100x + 25x2 = 720 Combine like terms: 7x + 7x = 14x 116 + 14x + 7x + 7x + -100x + 25x2 = 720 Combine like terms: 14x + 7x = 21x 116 + 21x + 7x + -100x + 25x2 = 720 Combine like terms: 21x + 7x = 28x 116 + 28x + -100x + 25x2 = 720 Combine like terms: 28x + -100x = -72x 116 + -72x + 25x2 = 720 Solving 116 + -72x + 25x2 = 720 Solving for variable 'x'. Reorder the terms: 116 + -720 + -72x + 25x2 = 720 + -720 Combine like terms: 116 + -720 = -604 -604 + -72x + 25x2 = 720 + -720 Combine like terms: 720 + -720 = 0 -604 + -72x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -24.16 + -2.88x + x2 = 0 Move the constant term to the right: Add '24.16' to each side of the equation. -24.16 + -2.88x + 24.16 + x2 = 0 + 24.16 Reorder the terms: -24.16 + 24.16 + -2.88x + x2 = 0 + 24.16 Combine like terms: -24.16 + 24.16 = 0.00 0.00 + -2.88x + x2 = 0 + 24.16 -2.88x + x2 = 0 + 24.16 Combine like terms: 0 + 24.16 = 24.16 -2.88x + x2 = 24.16 The x term is -2.88x. Take half its coefficient (-1.44). Square it (2.0736) and add it to both sides. Add '2.0736' to each side of the equation. -2.88x + 2.0736 + x2 = 24.16 + 2.0736 Reorder the terms: 2.0736 + -2.88x + x2 = 24.16 + 2.0736 Combine like terms: 24.16 + 2.0736 = 26.2336 2.0736 + -2.88x + x2 = 26.2336 Factor a perfect square on the left side: (x + -1.44)(x + -1.44) = 26.2336 Calculate the square root of the right side: 5.121874657 Break this problem into two subproblems by setting (x + -1.44) equal to 5.121874657 and -5.121874657.Subproblem 1
x + -1.44 = 5.121874657 Simplifying x + -1.44 = 5.121874657 Reorder the terms: -1.44 + x = 5.121874657 Solving -1.44 + x = 5.121874657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.44' to each side of the equation. -1.44 + 1.44 + x = 5.121874657 + 1.44 Combine like terms: -1.44 + 1.44 = 0.00 0.00 + x = 5.121874657 + 1.44 x = 5.121874657 + 1.44 Combine like terms: 5.121874657 + 1.44 = 6.561874657 x = 6.561874657 Simplifying x = 6.561874657Subproblem 2
x + -1.44 = -5.121874657 Simplifying x + -1.44 = -5.121874657 Reorder the terms: -1.44 + x = -5.121874657 Solving -1.44 + x = -5.121874657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.44' to each side of the equation. -1.44 + 1.44 + x = -5.121874657 + 1.44 Combine like terms: -1.44 + 1.44 = 0.00 0.00 + x = -5.121874657 + 1.44 x = -5.121874657 + 1.44 Combine like terms: -5.121874657 + 1.44 = -3.681874657 x = -3.681874657 Simplifying x = -3.681874657Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.561874657, -3.681874657}
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