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Simplifying 260 = 0.5(x)(x + -6) Reorder the terms: 260 = 0.5x(-6 + x) 260 = (-6 * 0.5x + x * 0.5x) 260 = (-3x + 0.5x2) Solving 260 = -3x + 0.5x2 Solving for variable 'x'. Reorder the terms: 260 + 3x + -0.5x2 = -3x + 3x + 0.5x2 + -0.5x2 Combine like terms: -3x + 3x = 0 260 + 3x + -0.5x2 = 0 + 0.5x2 + -0.5x2 260 + 3x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 260 + 3x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -520 + -6x + x2 = 0 Move the constant term to the right: Add '520' to each side of the equation. -520 + -6x + 520 + x2 = 0 + 520 Reorder the terms: -520 + 520 + -6x + x2 = 0 + 520 Combine like terms: -520 + 520 = 0 0 + -6x + x2 = 0 + 520 -6x + x2 = 0 + 520 Combine like terms: 0 + 520 = 520 -6x + x2 = 520 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 520 + 9 Reorder the terms: 9 + -6x + x2 = 520 + 9 Combine like terms: 520 + 9 = 529 9 + -6x + x2 = 529 Factor a perfect square on the left side: (x + -3)(x + -3) = 529 Calculate the square root of the right side: 23 Break this problem into two subproblems by setting (x + -3) equal to 23 and -23.Subproblem 1
x + -3 = 23 Simplifying x + -3 = 23 Reorder the terms: -3 + x = 23 Solving -3 + x = 23 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 23 + 3 Combine like terms: -3 + 3 = 0 0 + x = 23 + 3 x = 23 + 3 Combine like terms: 23 + 3 = 26 x = 26 Simplifying x = 26Subproblem 2
x + -3 = -23 Simplifying x + -3 = -23 Reorder the terms: -3 + x = -23 Solving -3 + x = -23 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -23 + 3 Combine like terms: -3 + 3 = 0 0 + x = -23 + 3 x = -23 + 3 Combine like terms: -23 + 3 = -20 x = -20 Simplifying x = -20Solution
The solution to the problem is based on the solutions from the subproblems. x = {26, -20}
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