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Simplifying 0.5(x + -2)(x) + -14 = 0 Reorder the terms: 0.5(-2 + x)(x) + -14 = 0 Reorder the terms for easier multiplication: 0.5x(-2 + x) + -14 = 0 (-2 * 0.5x + x * 0.5x) + -14 = 0 (-1x + 0.5x2) + -14 = 0 Reorder the terms: -14 + -1x + 0.5x2 = 0 Solving -14 + -1x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -28 + -2x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + -2x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -2x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -2x + x2 = 0 + 28 -2x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -2x + x2 = 28 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 = 28 + 1 Reorder the terms: 1 + -2x + x2 = 28 + 1 Combine like terms: 28 + 1 = 29 1 + -2x + x2 = 29 Factor a perfect square on the left side: (x + -1)(x + -1) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + -1) equal to 5.385164807 and -5.385164807.Subproblem 1
x + -1 = 5.385164807 Simplifying x + -1 = 5.385164807 Reorder the terms: -1 + x = 5.385164807 Solving -1 + x = 5.385164807 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 = 5.385164807 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.385164807 + 1 x = 5.385164807 + 1 Combine like terms: 5.385164807 + 1 = 6.385164807 x = 6.385164807 Simplifying x = 6.385164807Subproblem 2
x + -1 = -5.385164807 Simplifying x + -1 = -5.385164807 Reorder the terms: -1 + x = -5.385164807 Solving -1 + x = -5.385164807 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 = -5.385164807 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.385164807 + 1 x = -5.385164807 + 1 Combine like terms: -5.385164807 + 1 = -4.385164807 x = -4.385164807 Simplifying x = -4.385164807Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.385164807, -4.385164807}
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