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Simplifying x2 + 7.5x = 4 Reorder the terms: 7.5x + x2 = 4 Solving 7.5x + x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + 7.5x + x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 7.5x + x2 = 0 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 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 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 = -8 x = -8 Simplifying x = -8Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, -8}
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