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Simplifying 2x2 = 15x + 25 Reorder the terms: 2x2 = 25 + 15x Solving 2x2 = 25 + 15x Solving for variable 'x'. Reorder the terms: -25 + -15x + 2x2 = 25 + 15x + -25 + -15x Reorder the terms: -25 + -15x + 2x2 = 25 + -25 + 15x + -15x Combine like terms: 25 + -25 = 0 -25 + -15x + 2x2 = 0 + 15x + -15x -25 + -15x + 2x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -25 + -15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + -7.5x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -7.5x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -7.5x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -7.5x + x2 = 0 + 12.5 -7.5x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -7.5x + x2 = 12.5 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 12.5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 12.5 + 14.0625 Combine like terms: 12.5 + 14.0625 = 26.5625 14.0625 + -7.5x + x2 = 26.5625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 26.5625 Calculate the square root of the right side: 5.153882032 Break this problem into two subproblems by setting (x + -3.75) equal to 5.153882032 and -5.153882032.Subproblem 1
x + -3.75 = 5.153882032 Simplifying x + -3.75 = 5.153882032 Reorder the terms: -3.75 + x = 5.153882032 Solving -3.75 + x = 5.153882032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 5.153882032 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 5.153882032 + 3.75 x = 5.153882032 + 3.75 Combine like terms: 5.153882032 + 3.75 = 8.903882032 x = 8.903882032 Simplifying x = 8.903882032Subproblem 2
x + -3.75 = -5.153882032 Simplifying x + -3.75 = -5.153882032 Reorder the terms: -3.75 + x = -5.153882032 Solving -3.75 + x = -5.153882032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -5.153882032 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -5.153882032 + 3.75 x = -5.153882032 + 3.75 Combine like terms: -5.153882032 + 3.75 = -1.403882032 x = -1.403882032 Simplifying x = -1.403882032Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.903882032, -1.403882032}
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