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Simplifying x2 + 30x + -1220 = 0 Reorder the terms: -1220 + 30x + x2 = 0 Solving -1220 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1220' to each side of the equation. -1220 + 30x + 1220 + x2 = 0 + 1220 Reorder the terms: -1220 + 1220 + 30x + x2 = 0 + 1220 Combine like terms: -1220 + 1220 = 0 0 + 30x + x2 = 0 + 1220 30x + x2 = 0 + 1220 Combine like terms: 0 + 1220 = 1220 30x + x2 = 1220 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 = 1220 + 225 Reorder the terms: 225 + 30x + x2 = 1220 + 225 Combine like terms: 1220 + 225 = 1445 225 + 30x + x2 = 1445 Factor a perfect square on the left side: (x + 15)(x + 15) = 1445 Calculate the square root of the right side: 38.013155617 Break this problem into two subproblems by setting (x + 15) equal to 38.013155617 and -38.013155617.Subproblem 1
x + 15 = 38.013155617 Simplifying x + 15 = 38.013155617 Reorder the terms: 15 + x = 38.013155617 Solving 15 + x = 38.013155617 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 = 38.013155617 + -15 Combine like terms: 15 + -15 = 0 0 + x = 38.013155617 + -15 x = 38.013155617 + -15 Combine like terms: 38.013155617 + -15 = 23.013155617 x = 23.013155617 Simplifying x = 23.013155617Subproblem 2
x + 15 = -38.013155617 Simplifying x + 15 = -38.013155617 Reorder the terms: 15 + x = -38.013155617 Solving 15 + x = -38.013155617 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 = -38.013155617 + -15 Combine like terms: 15 + -15 = 0 0 + x = -38.013155617 + -15 x = -38.013155617 + -15 Combine like terms: -38.013155617 + -15 = -53.013155617 x = -53.013155617 Simplifying x = -53.013155617Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.013155617, -53.013155617}
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