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Simplifying 5x(4 + x) = 175 + x (4 * 5x + x * 5x) = 175 + x (20x + 5x2) = 175 + x Solving 20x + 5x2 = 175 + x Solving for variable 'x'. Reorder the terms: -175 + 20x + -1x + 5x2 = 175 + x + -175 + -1x Combine like terms: 20x + -1x = 19x -175 + 19x + 5x2 = 175 + x + -175 + -1x Reorder the terms: -175 + 19x + 5x2 = 175 + -175 + x + -1x Combine like terms: 175 + -175 = 0 -175 + 19x + 5x2 = 0 + x + -1x -175 + 19x + 5x2 = x + -1x Combine like terms: x + -1x = 0 -175 + 19x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -35 + 3.8x + x2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + 3.8x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + 3.8x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 3.8x + x2 = 0 + 35 3.8x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 3.8x + x2 = 35 The x term is 3.8x. Take half its coefficient (1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. 3.8x + 3.61 + x2 = 35 + 3.61 Reorder the terms: 3.61 + 3.8x + x2 = 35 + 3.61 Combine like terms: 35 + 3.61 = 38.61 3.61 + 3.8x + x2 = 38.61 Factor a perfect square on the left side: (x + 1.9)(x + 1.9) = 38.61 Calculate the square root of the right side: 6.213694553 Break this problem into two subproblems by setting (x + 1.9) equal to 6.213694553 and -6.213694553.Subproblem 1
x + 1.9 = 6.213694553 Simplifying x + 1.9 = 6.213694553 Reorder the terms: 1.9 + x = 6.213694553 Solving 1.9 + x = 6.213694553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = 6.213694553 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 6.213694553 + -1.9 x = 6.213694553 + -1.9 Combine like terms: 6.213694553 + -1.9 = 4.313694553 x = 4.313694553 Simplifying x = 4.313694553Subproblem 2
x + 1.9 = -6.213694553 Simplifying x + 1.9 = -6.213694553 Reorder the terms: 1.9 + x = -6.213694553 Solving 1.9 + x = -6.213694553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = -6.213694553 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -6.213694553 + -1.9 x = -6.213694553 + -1.9 Combine like terms: -6.213694553 + -1.9 = -8.113694553 x = -8.113694553 Simplifying x = -8.113694553Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.313694553, -8.113694553}
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