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Simplifying x2 + -15x + 54 = 155 Reorder the terms: 54 + -15x + x2 = 155 Solving 54 + -15x + x2 = 155 Solving for variable 'x'. Reorder the terms: 54 + -155 + -15x + x2 = 155 + -155 Combine like terms: 54 + -155 = -101 -101 + -15x + x2 = 155 + -155 Combine like terms: 155 + -155 = 0 -101 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '101' to each side of the equation. -101 + -15x + 101 + x2 = 0 + 101 Reorder the terms: -101 + 101 + -15x + x2 = 0 + 101 Combine like terms: -101 + 101 = 0 0 + -15x + x2 = 0 + 101 -15x + x2 = 0 + 101 Combine like terms: 0 + 101 = 101 -15x + x2 = 101 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 101 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 101 + 56.25 Combine like terms: 101 + 56.25 = 157.25 56.25 + -15x + x2 = 157.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 157.25 Calculate the square root of the right side: 12.539936204 Break this problem into two subproblems by setting (x + -7.5) equal to 12.539936204 and -12.539936204.Subproblem 1
x + -7.5 = 12.539936204 Simplifying x + -7.5 = 12.539936204 Reorder the terms: -7.5 + x = 12.539936204 Solving -7.5 + x = 12.539936204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 12.539936204 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 12.539936204 + 7.5 x = 12.539936204 + 7.5 Combine like terms: 12.539936204 + 7.5 = 20.039936204 x = 20.039936204 Simplifying x = 20.039936204Subproblem 2
x + -7.5 = -12.539936204 Simplifying x + -7.5 = -12.539936204 Reorder the terms: -7.5 + x = -12.539936204 Solving -7.5 + x = -12.539936204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -12.539936204 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -12.539936204 + 7.5 x = -12.539936204 + 7.5 Combine like terms: -12.539936204 + 7.5 = -5.039936204 x = -5.039936204 Simplifying x = -5.039936204Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.039936204, -5.039936204}
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