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Simplifying 3(x + 5) = 2x(x + 10) Reorder the terms: 3(5 + x) = 2x(x + 10) (5 * 3 + x * 3) = 2x(x + 10) (15 + 3x) = 2x(x + 10) Reorder the terms: 15 + 3x = 2x(10 + x) 15 + 3x = (10 * 2x + x * 2x) 15 + 3x = (20x + 2x2) Solving 15 + 3x = 20x + 2x2 Solving for variable 'x'. Combine like terms: 3x + -20x = -17x 15 + -17x + -2x2 = 20x + 2x2 + -20x + -2x2 Reorder the terms: 15 + -17x + -2x2 = 20x + -20x + 2x2 + -2x2 Combine like terms: 20x + -20x = 0 15 + -17x + -2x2 = 0 + 2x2 + -2x2 15 + -17x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 15 + -17x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -7.5 + 8.5x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 8.5x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 8.5x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 8.5x + x2 = 0 + 7.5 8.5x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 8.5x + x2 = 7.5 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = 7.5 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 7.5 + 18.0625 Combine like terms: 7.5 + 18.0625 = 25.5625 18.0625 + 8.5x + x2 = 25.5625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 25.5625 Calculate the square root of the right side: 5.055937104 Break this problem into two subproblems by setting (x + 4.25) equal to 5.055937104 and -5.055937104.Subproblem 1
x + 4.25 = 5.055937104 Simplifying x + 4.25 = 5.055937104 Reorder the terms: 4.25 + x = 5.055937104 Solving 4.25 + x = 5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 5.055937104 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 5.055937104 + -4.25 x = 5.055937104 + -4.25 Combine like terms: 5.055937104 + -4.25 = 0.805937104 x = 0.805937104 Simplifying x = 0.805937104Subproblem 2
x + 4.25 = -5.055937104 Simplifying x + 4.25 = -5.055937104 Reorder the terms: 4.25 + x = -5.055937104 Solving 4.25 + x = -5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -5.055937104 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -5.055937104 + -4.25 x = -5.055937104 + -4.25 Combine like terms: -5.055937104 + -4.25 = -9.305937104 x = -9.305937104 Simplifying x = -9.305937104Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.805937104, -9.305937104}
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