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Simplifying 5x + -3 = 0.5(x2 + 5x) Reorder the terms: -3 + 5x = 0.5(x2 + 5x) Reorder the terms: -3 + 5x = 0.5(5x + x2) -3 + 5x = (5x * 0.5 + x2 * 0.5) -3 + 5x = (2.5x + 0.5x2) Solving -3 + 5x = 2.5x + 0.5x2 Solving for variable 'x'. Combine like terms: 5x + -2.5x = 2.5x -3 + 2.5x + -0.5x2 = 2.5x + 0.5x2 + -2.5x + -0.5x2 Reorder the terms: -3 + 2.5x + -0.5x2 = 2.5x + -2.5x + 0.5x2 + -0.5x2 Combine like terms: 2.5x + -2.5x = 0.0 -3 + 2.5x + -0.5x2 = 0.0 + 0.5x2 + -0.5x2 -3 + 2.5x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 -3 + 2.5x + -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'. 6 + -5x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -5x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -5x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5x + x2 = 0 + -6 -5x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -5x + x2 = -6 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -6 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -6 + 6.25 Combine like terms: -6 + 6.25 = 0.25 6.25 + -5x + x2 = 0.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 0.25 Calculate the square root of the right side: 0.5 Break this problem into two subproblems by setting (x + -2.5) equal to 0.5 and -0.5.Subproblem 1
x + -2.5 = 0.5 Simplifying x + -2.5 = 0.5 Reorder the terms: -2.5 + x = 0.5 Solving -2.5 + x = 0.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 0.5 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 0.5 + 2.5 x = 0.5 + 2.5 Combine like terms: 0.5 + 2.5 = 3 x = 3 Simplifying x = 3Subproblem 2
x + -2.5 = -0.5 Simplifying x + -2.5 = -0.5 Reorder the terms: -2.5 + x = -0.5 Solving -2.5 + x = -0.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -0.5 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -0.5 + 2.5 x = -0.5 + 2.5 Combine like terms: -0.5 + 2.5 = 2 x = 2 Simplifying x = 2Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, 2}
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