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Simplifying 5x2 + -10x + 25 = 48 Reorder the terms: 25 + -10x + 5x2 = 48 Solving 25 + -10x + 5x2 = 48 Solving for variable 'x'. Reorder the terms: 25 + -48 + -10x + 5x2 = 48 + -48 Combine like terms: 25 + -48 = -23 -23 + -10x + 5x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -23 + -10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.6 + -2x + x2 = 0 Move the constant term to the right: Add '4.6' to each side of the equation. -4.6 + -2x + 4.6 + x2 = 0 + 4.6 Reorder the terms: -4.6 + 4.6 + -2x + x2 = 0 + 4.6 Combine like terms: -4.6 + 4.6 = 0.0 0.0 + -2x + x2 = 0 + 4.6 -2x + x2 = 0 + 4.6 Combine like terms: 0 + 4.6 = 4.6 -2x + x2 = 4.6 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 4.6 + 1 Reorder the terms: 1 + -2x + x2 = 4.6 + 1 Combine like terms: 4.6 + 1 = 5.6 1 + -2x + x2 = 5.6 Factor a perfect square on the left side: (x + -1)(x + -1) = 5.6 Calculate the square root of the right side: 2.366431913 Break this problem into two subproblems by setting (x + -1) equal to 2.366431913 and -2.366431913.Subproblem 1
x + -1 = 2.366431913 Simplifying x + -1 = 2.366431913 Reorder the terms: -1 + x = 2.366431913 Solving -1 + x = 2.366431913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.366431913 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.366431913 + 1 x = 2.366431913 + 1 Combine like terms: 2.366431913 + 1 = 3.366431913 x = 3.366431913 Simplifying x = 3.366431913Subproblem 2
x + -1 = -2.366431913 Simplifying x + -1 = -2.366431913 Reorder the terms: -1 + x = -2.366431913 Solving -1 + x = -2.366431913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.366431913 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.366431913 + 1 x = -2.366431913 + 1 Combine like terms: -2.366431913 + 1 = -1.366431913 x = -1.366431913 Simplifying x = -1.366431913Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.366431913, -1.366431913}
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