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Simplifying x2 + -1x + -8.75 = 0 Reorder the terms: -8.75 + -1x + x2 = 0 Solving -8.75 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + -1x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + -1x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + -1x + x2 = 0 + 8.75 -1x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 -1x + x2 = 8.75 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 8.75 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 8.75 + 0.25 Combine like terms: 8.75 + 0.25 = 9 0.25 + -1x + x2 = 9 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 9 Calculate the square root of the right side: 3 Break this problem into two subproblems by setting (x + -0.5) equal to 3 and -3.Subproblem 1
x + -0.5 = 3 Simplifying x + -0.5 = 3 Reorder the terms: -0.5 + x = 3 Solving -0.5 + x = 3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3 + 0.5 x = 3 + 0.5 Combine like terms: 3 + 0.5 = 3.5 x = 3.5 Simplifying x = 3.5Subproblem 2
x + -0.5 = -3 Simplifying x + -0.5 = -3 Reorder the terms: -0.5 + x = -3 Solving -0.5 + x = -3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3 + 0.5 x = -3 + 0.5 Combine like terms: -3 + 0.5 = -2.5 x = -2.5 Simplifying x = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5, -2.5}
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