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Simplifying x2 + 30x = 90 Reorder the terms: 30x + x2 = 90 Solving 30x + x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + 30x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 30x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 30x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 30x + x2 = 0 + 90 30x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 30x + x2 = 90 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 = 90 + 225 Reorder the terms: 225 + 30x + x2 = 90 + 225 Combine like terms: 90 + 225 = 315 225 + 30x + x2 = 315 Factor a perfect square on the left side: (x + 15)(x + 15) = 315 Calculate the square root of the right side: 17.748239349 Break this problem into two subproblems by setting (x + 15) equal to 17.748239349 and -17.748239349.Subproblem 1
x + 15 = 17.748239349 Simplifying x + 15 = 17.748239349 Reorder the terms: 15 + x = 17.748239349 Solving 15 + x = 17.748239349 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 = 17.748239349 + -15 Combine like terms: 15 + -15 = 0 0 + x = 17.748239349 + -15 x = 17.748239349 + -15 Combine like terms: 17.748239349 + -15 = 2.748239349 x = 2.748239349 Simplifying x = 2.748239349Subproblem 2
x + 15 = -17.748239349 Simplifying x + 15 = -17.748239349 Reorder the terms: 15 + x = -17.748239349 Solving 15 + x = -17.748239349 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 = -17.748239349 + -15 Combine like terms: 15 + -15 = 0 0 + x = -17.748239349 + -15 x = -17.748239349 + -15 Combine like terms: -17.748239349 + -15 = -32.748239349 x = -32.748239349 Simplifying x = -32.748239349Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.748239349, -32.748239349}
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