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Simplifying 23 + -10x + -5x2 = 0 Solving 23 + -10x + -5x2 = 0 Solving for variable 'x'. 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 = 1.366431913 x = 1.366431913 Simplifying x = 1.366431913Subproblem 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 = -3.366431913 x = -3.366431913 Simplifying x = -3.366431913Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.366431913, -3.366431913}
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