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Simplifying 30x + x2 = 56 Solving 30x + x2 = 56 Solving for variable 'x'. Reorder the terms: -56 + 30x + x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 30x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + 30x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 30x + x2 = 0 + 56 30x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 30x + x2 = 56 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 = 56 + 225 Reorder the terms: 225 + 30x + x2 = 56 + 225 Combine like terms: 56 + 225 = 281 225 + 30x + x2 = 281 Factor a perfect square on the left side: (x + 15)(x + 15) = 281 Calculate the square root of the right side: 16.763054614 Break this problem into two subproblems by setting (x + 15) equal to 16.763054614 and -16.763054614.Subproblem 1
x + 15 = 16.763054614 Simplifying x + 15 = 16.763054614 Reorder the terms: 15 + x = 16.763054614 Solving 15 + x = 16.763054614 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 = 16.763054614 + -15 Combine like terms: 15 + -15 = 0 0 + x = 16.763054614 + -15 x = 16.763054614 + -15 Combine like terms: 16.763054614 + -15 = 1.763054614 x = 1.763054614 Simplifying x = 1.763054614Subproblem 2
x + 15 = -16.763054614 Simplifying x + 15 = -16.763054614 Reorder the terms: 15 + x = -16.763054614 Solving 15 + x = -16.763054614 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 = -16.763054614 + -15 Combine like terms: 15 + -15 = 0 0 + x = -16.763054614 + -15 x = -16.763054614 + -15 Combine like terms: -16.763054614 + -15 = -31.763054614 x = -31.763054614 Simplifying x = -31.763054614Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.763054614, -31.763054614}
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