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Simplifying x2 + 30x + -28 = 0 Reorder the terms: -28 + 30x + x2 = 0 Solving -28 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 30x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 30x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 30x + x2 = 0 + 28 30x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 30x + x2 = 28 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 = 28 + 225 Reorder the terms: 225 + 30x + x2 = 28 + 225 Combine like terms: 28 + 225 = 253 225 + 30x + x2 = 253 Factor a perfect square on the left side: (x + 15)(x + 15) = 253 Calculate the square root of the right side: 15.905973721 Break this problem into two subproblems by setting (x + 15) equal to 15.905973721 and -15.905973721.Subproblem 1
x + 15 = 15.905973721 Simplifying x + 15 = 15.905973721 Reorder the terms: 15 + x = 15.905973721 Solving 15 + x = 15.905973721 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 = 15.905973721 + -15 Combine like terms: 15 + -15 = 0 0 + x = 15.905973721 + -15 x = 15.905973721 + -15 Combine like terms: 15.905973721 + -15 = 0.905973721 x = 0.905973721 Simplifying x = 0.905973721Subproblem 2
x + 15 = -15.905973721 Simplifying x + 15 = -15.905973721 Reorder the terms: 15 + x = -15.905973721 Solving 15 + x = -15.905973721 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 = -15.905973721 + -15 Combine like terms: 15 + -15 = 0 0 + x = -15.905973721 + -15 x = -15.905973721 + -15 Combine like terms: -15.905973721 + -15 = -30.905973721 x = -30.905973721 Simplifying x = -30.905973721Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.905973721, -30.905973721}
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