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Simplifying x2 + 30x + -1600 = 0 Reorder the terms: -1600 + 30x + x2 = 0 Solving -1600 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1600' to each side of the equation. -1600 + 30x + 1600 + x2 = 0 + 1600 Reorder the terms: -1600 + 1600 + 30x + x2 = 0 + 1600 Combine like terms: -1600 + 1600 = 0 0 + 30x + x2 = 0 + 1600 30x + x2 = 0 + 1600 Combine like terms: 0 + 1600 = 1600 30x + x2 = 1600 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 = 1600 + 225 Reorder the terms: 225 + 30x + x2 = 1600 + 225 Combine like terms: 1600 + 225 = 1825 225 + 30x + x2 = 1825 Factor a perfect square on the left side: (x + 15)(x + 15) = 1825 Calculate the square root of the right side: 42.720018727 Break this problem into two subproblems by setting (x + 15) equal to 42.720018727 and -42.720018727.Subproblem 1
x + 15 = 42.720018727 Simplifying x + 15 = 42.720018727 Reorder the terms: 15 + x = 42.720018727 Solving 15 + x = 42.720018727 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 = 42.720018727 + -15 Combine like terms: 15 + -15 = 0 0 + x = 42.720018727 + -15 x = 42.720018727 + -15 Combine like terms: 42.720018727 + -15 = 27.720018727 x = 27.720018727 Simplifying x = 27.720018727Subproblem 2
x + 15 = -42.720018727 Simplifying x + 15 = -42.720018727 Reorder the terms: 15 + x = -42.720018727 Solving 15 + x = -42.720018727 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 = -42.720018727 + -15 Combine like terms: 15 + -15 = 0 0 + x = -42.720018727 + -15 x = -42.720018727 + -15 Combine like terms: -42.720018727 + -15 = -57.720018727 x = -57.720018727 Simplifying x = -57.720018727Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.720018727, -57.720018727}
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