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Simplifying (2x + 7) * x = 45 Reorder the terms: (7 + 2x) * x = 45 Reorder the terms for easier multiplication: x(7 + 2x) = 45 (7 * x + 2x * x) = 45 (7x + 2x2) = 45 Solving 7x + 2x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + 7x + 2x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -22.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + 3.5x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + 3.5x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + 3.5x + x2 = 0 + 22.5 3.5x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 3.5x + x2 = 22.5 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 = 22.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 22.5 + 3.0625 Combine like terms: 22.5 + 3.0625 = 25.5625 3.0625 + 3.5x + x2 = 25.5625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 25.5625 Calculate the square root of the right side: 5.055937104 Break this problem into two subproblems by setting (x + 1.75) equal to 5.055937104 and -5.055937104.Subproblem 1
x + 1.75 = 5.055937104 Simplifying x + 1.75 = 5.055937104 Reorder the terms: 1.75 + x = 5.055937104 Solving 1.75 + x = 5.055937104 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 = 5.055937104 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 5.055937104 + -1.75 x = 5.055937104 + -1.75 Combine like terms: 5.055937104 + -1.75 = 3.305937104 x = 3.305937104 Simplifying x = 3.305937104Subproblem 2
x + 1.75 = -5.055937104 Simplifying x + 1.75 = -5.055937104 Reorder the terms: 1.75 + x = -5.055937104 Solving 1.75 + x = -5.055937104 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 = -5.055937104 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -5.055937104 + -1.75 x = -5.055937104 + -1.75 Combine like terms: -5.055937104 + -1.75 = -6.805937104 x = -6.805937104 Simplifying x = -6.805937104Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.305937104, -6.805937104}
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