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Simplifying x2 + -7.5x + -4 = 0 Reorder the terms: -4 + -7.5x + x2 = 0 Solving -4 + -7.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -7.5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -7.5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7.5x + x2 = 0 + 4 -7.5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -7.5x + x2 = 4 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 4 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 4 + 14.0625 Combine like terms: 4 + 14.0625 = 18.0625 14.0625 + -7.5x + x2 = 18.0625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 18.0625 Calculate the square root of the right side: 4.25 Break this problem into two subproblems by setting (x + -3.75) equal to 4.25 and -4.25.Subproblem 1
x + -3.75 = 4.25 Simplifying x + -3.75 = 4.25 Reorder the terms: -3.75 + x = 4.25 Solving -3.75 + x = 4.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 4.25 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 4.25 + 3.75 x = 4.25 + 3.75 Combine like terms: 4.25 + 3.75 = 8 x = 8 Simplifying x = 8Subproblem 2
x + -3.75 = -4.25 Simplifying x + -3.75 = -4.25 Reorder the terms: -3.75 + x = -4.25 Solving -3.75 + x = -4.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -4.25 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -4.25 + 3.75 x = -4.25 + 3.75 Combine like terms: -4.25 + 3.75 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, -0.5}
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