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Simplifying x2 + 30x + 75 = 7 Reorder the terms: 75 + 30x + x2 = 7 Solving 75 + 30x + x2 = 7 Solving for variable 'x'. Reorder the terms: 75 + -7 + 30x + x2 = 7 + -7 Combine like terms: 75 + -7 = 68 68 + 30x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 68 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-68' to each side of the equation. 68 + 30x + -68 + x2 = 0 + -68 Reorder the terms: 68 + -68 + 30x + x2 = 0 + -68 Combine like terms: 68 + -68 = 0 0 + 30x + x2 = 0 + -68 30x + x2 = 0 + -68 Combine like terms: 0 + -68 = -68 30x + x2 = -68 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = -68 + 225 Reorder the terms: 225 + 30x + x2 = -68 + 225 Combine like terms: -68 + 225 = 157 225 + 30x + x2 = 157 Factor a perfect square on the left side: (x + 15)(x + 15) = 157 Calculate the square root of the right side: 12.529964086 Break this problem into two subproblems by setting (x + 15) equal to 12.529964086 and -12.529964086.Subproblem 1
x + 15 = 12.529964086 Simplifying x + 15 = 12.529964086 Reorder the terms: 15 + x = 12.529964086 Solving 15 + x = 12.529964086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 12.529964086 + -15 Combine like terms: 15 + -15 = 0 0 + x = 12.529964086 + -15 x = 12.529964086 + -15 Combine like terms: 12.529964086 + -15 = -2.470035914 x = -2.470035914 Simplifying x = -2.470035914Subproblem 2
x + 15 = -12.529964086 Simplifying x + 15 = -12.529964086 Reorder the terms: 15 + x = -12.529964086 Solving 15 + x = -12.529964086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -12.529964086 + -15 Combine like terms: 15 + -15 = 0 0 + x = -12.529964086 + -15 x = -12.529964086 + -15 Combine like terms: -12.529964086 + -15 = -27.529964086 x = -27.529964086 Simplifying x = -27.529964086Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.470035914, -27.529964086}
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