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Simplifying x2 + -30x + 45 = 0 Reorder the terms: 45 + -30x + x2 = 0 Solving 45 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + -30x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + -30x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -30x + x2 = 0 + -45 -30x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 -30x + x2 = -45 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 = -45 + 225 Reorder the terms: 225 + -30x + x2 = -45 + 225 Combine like terms: -45 + 225 = 180 225 + -30x + x2 = 180 Factor a perfect square on the left side: (x + -15)(x + -15) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (x + -15) equal to 13.416407865 and -13.416407865.Subproblem 1
x + -15 = 13.416407865 Simplifying x + -15 = 13.416407865 Reorder the terms: -15 + x = 13.416407865 Solving -15 + x = 13.416407865 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 = 13.416407865 + 15 Combine like terms: -15 + 15 = 0 0 + x = 13.416407865 + 15 x = 13.416407865 + 15 Combine like terms: 13.416407865 + 15 = 28.416407865 x = 28.416407865 Simplifying x = 28.416407865Subproblem 2
x + -15 = -13.416407865 Simplifying x + -15 = -13.416407865 Reorder the terms: -15 + x = -13.416407865 Solving -15 + x = -13.416407865 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 = -13.416407865 + 15 Combine like terms: -15 + 15 = 0 0 + x = -13.416407865 + 15 x = -13.416407865 + 15 Combine like terms: -13.416407865 + 15 = 1.583592135 x = 1.583592135 Simplifying x = 1.583592135Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.416407865, 1.583592135}
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