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Simplifying 0.5(x + 2)(x) = 15 Reorder the terms: 0.5(2 + x)(x) = 15 Reorder the terms for easier multiplication: 0.5x(2 + x) = 15 (2 * 0.5x + x * 0.5x) = 15 (1x + 0.5x2) = 15 Solving 1x + 0.5x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 1x + 0.5x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 1x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -30 + 2x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 2x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 2x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 2x + x2 = 0 + 30 2x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 2x + x2 = 30 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 = 30 + 1 Reorder the terms: 1 + 2x + x2 = 30 + 1 Combine like terms: 30 + 1 = 31 1 + 2x + x2 = 31 Factor a perfect square on the left side: (x + 1)(x + 1) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + 1) equal to 5.567764363 and -5.567764363.Subproblem 1
x + 1 = 5.567764363 Simplifying x + 1 = 5.567764363 Reorder the terms: 1 + x = 5.567764363 Solving 1 + x = 5.567764363 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 = 5.567764363 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.567764363 + -1 x = 5.567764363 + -1 Combine like terms: 5.567764363 + -1 = 4.567764363 x = 4.567764363 Simplifying x = 4.567764363Subproblem 2
x + 1 = -5.567764363 Simplifying x + 1 = -5.567764363 Reorder the terms: 1 + x = -5.567764363 Solving 1 + x = -5.567764363 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 = -5.567764363 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.567764363 + -1 x = -5.567764363 + -1 Combine like terms: -5.567764363 + -1 = -6.567764363 x = -6.567764363 Simplifying x = -6.567764363Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.567764363, -6.567764363}
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