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Simplifying 2x2 + 14x = 5x + 15 Reorder the terms: 14x + 2x2 = 5x + 15 Reorder the terms: 14x + 2x2 = 15 + 5x Solving 14x + 2x2 = 15 + 5x Solving for variable 'x'. Reorder the terms: -15 + 14x + -5x + 2x2 = 15 + 5x + -15 + -5x Combine like terms: 14x + -5x = 9x -15 + 9x + 2x2 = 15 + 5x + -15 + -5x Reorder the terms: -15 + 9x + 2x2 = 15 + -15 + 5x + -5x Combine like terms: 15 + -15 = 0 -15 + 9x + 2x2 = 0 + 5x + -5x -15 + 9x + 2x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -15 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 4.5x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 4.5x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 4.5x + x2 = 0 + 7.5 4.5x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 4.5x + x2 = 7.5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 7.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 7.5 + 5.0625 Combine like terms: 7.5 + 5.0625 = 12.5625 5.0625 + 4.5x + x2 = 12.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (x + 2.25) equal to 3.54436172 and -3.54436172.Subproblem 1
x + 2.25 = 3.54436172 Simplifying x + 2.25 = 3.54436172 Reorder the terms: 2.25 + x = 3.54436172 Solving 2.25 + x = 3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 3.54436172 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.54436172 + -2.25 x = 3.54436172 + -2.25 Combine like terms: 3.54436172 + -2.25 = 1.29436172 x = 1.29436172 Simplifying x = 1.29436172Subproblem 2
x + 2.25 = -3.54436172 Simplifying x + 2.25 = -3.54436172 Reorder the terms: 2.25 + x = -3.54436172 Solving 2.25 + x = -3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -3.54436172 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.54436172 + -2.25 x = -3.54436172 + -2.25 Combine like terms: -3.54436172 + -2.25 = -5.79436172 x = -5.79436172 Simplifying x = -5.79436172Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.29436172, -5.79436172}
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