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Simplifying 354 = x + x(x + 14) Reorder the terms: 354 = x + x(14 + x) 354 = x + (14 * x + x * x) 354 = x + (14x + x2) Combine like terms: x + 14x = 15x 354 = 15x + x2 Solving 354 = 15x + x2 Solving for variable 'x'. Reorder the terms: 354 + -15x + -1x2 = 15x + -15x + x2 + -1x2 Combine like terms: 15x + -15x = 0 354 + -15x + -1x2 = 0 + x2 + -1x2 354 + -15x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 354 + -15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -354 + 15x + x2 = 0 Move the constant term to the right: Add '354' to each side of the equation. -354 + 15x + 354 + x2 = 0 + 354 Reorder the terms: -354 + 354 + 15x + x2 = 0 + 354 Combine like terms: -354 + 354 = 0 0 + 15x + x2 = 0 + 354 15x + x2 = 0 + 354 Combine like terms: 0 + 354 = 354 15x + x2 = 354 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 354 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 354 + 56.25 Combine like terms: 354 + 56.25 = 410.25 56.25 + 15x + x2 = 410.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 410.25 Calculate the square root of the right side: 20.254629101 Break this problem into two subproblems by setting (x + 7.5) equal to 20.254629101 and -20.254629101.Subproblem 1
x + 7.5 = 20.254629101 Simplifying x + 7.5 = 20.254629101 Reorder the terms: 7.5 + x = 20.254629101 Solving 7.5 + x = 20.254629101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 20.254629101 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 20.254629101 + -7.5 x = 20.254629101 + -7.5 Combine like terms: 20.254629101 + -7.5 = 12.754629101 x = 12.754629101 Simplifying x = 12.754629101Subproblem 2
x + 7.5 = -20.254629101 Simplifying x + 7.5 = -20.254629101 Reorder the terms: 7.5 + x = -20.254629101 Solving 7.5 + x = -20.254629101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -20.254629101 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -20.254629101 + -7.5 x = -20.254629101 + -7.5 Combine like terms: -20.254629101 + -7.5 = -27.754629101 x = -27.754629101 Simplifying x = -27.754629101Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.754629101, -27.754629101}
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