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Simplifying x2 + 4x + -45 = 270 Reorder the terms: -45 + 4x + x2 = 270 Solving -45 + 4x + x2 = 270 Solving for variable 'x'. Reorder the terms: -45 + -270 + 4x + x2 = 270 + -270 Combine like terms: -45 + -270 = -315 -315 + 4x + x2 = 270 + -270 Combine like terms: 270 + -270 = 0 -315 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '315' to each side of the equation. -315 + 4x + 315 + x2 = 0 + 315 Reorder the terms: -315 + 315 + 4x + x2 = 0 + 315 Combine like terms: -315 + 315 = 0 0 + 4x + x2 = 0 + 315 4x + x2 = 0 + 315 Combine like terms: 0 + 315 = 315 4x + x2 = 315 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 315 + 4 Reorder the terms: 4 + 4x + x2 = 315 + 4 Combine like terms: 315 + 4 = 319 4 + 4x + x2 = 319 Factor a perfect square on the left side: (x + 2)(x + 2) = 319 Calculate the square root of the right side: 17.860571099 Break this problem into two subproblems by setting (x + 2) equal to 17.860571099 and -17.860571099.Subproblem 1
x + 2 = 17.860571099 Simplifying x + 2 = 17.860571099 Reorder the terms: 2 + x = 17.860571099 Solving 2 + x = 17.860571099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 17.860571099 + -2 Combine like terms: 2 + -2 = 0 0 + x = 17.860571099 + -2 x = 17.860571099 + -2 Combine like terms: 17.860571099 + -2 = 15.860571099 x = 15.860571099 Simplifying x = 15.860571099Subproblem 2
x + 2 = -17.860571099 Simplifying x + 2 = -17.860571099 Reorder the terms: 2 + x = -17.860571099 Solving 2 + x = -17.860571099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -17.860571099 + -2 Combine like terms: 2 + -2 = 0 0 + x = -17.860571099 + -2 x = -17.860571099 + -2 Combine like terms: -17.860571099 + -2 = -19.860571099 x = -19.860571099 Simplifying x = -19.860571099Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.860571099, -19.860571099}
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