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Simplifying 0.5x(2x + -1) = 60 Reorder the terms: 0.5x(-1 + 2x) = 60 (-1 * 0.5x + 2x * 0.5x) = 60 (-0.5x + 1x2) = 60 Solving -0.5x + 1x2 = 60 Solving for variable 'x'. Reorder the terms: -60 + -0.5x + 1x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + -0.5x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -0.5x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -0.5x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -0.5x + x2 = 0 + 60 -0.5x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -0.5x + x2 = 60 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 60 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 60 + 0.0625 Combine like terms: 60 + 0.0625 = 60.0625 0.0625 + -0.5x + x2 = 60.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 60.0625 Calculate the square root of the right side: 7.75 Break this problem into two subproblems by setting (x + -0.25) equal to 7.75 and -7.75.Subproblem 1
x + -0.25 = 7.75 Simplifying x + -0.25 = 7.75 Reorder the terms: -0.25 + x = 7.75 Solving -0.25 + x = 7.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 7.75 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 7.75 + 0.25 x = 7.75 + 0.25 Combine like terms: 7.75 + 0.25 = 8 x = 8 Simplifying x = 8Subproblem 2
x + -0.25 = -7.75 Simplifying x + -0.25 = -7.75 Reorder the terms: -0.25 + x = -7.75 Solving -0.25 + x = -7.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -7.75 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -7.75 + 0.25 x = -7.75 + 0.25 Combine like terms: -7.75 + 0.25 = -7.5 x = -7.5 Simplifying x = -7.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, -7.5}
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