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Simplifying 0 = x2 + 5x + -315 Reorder the terms: 0 = -315 + 5x + x2 Solving 0 = -315 + 5x + x2 Solving for variable 'x'. Combine like terms: 0 + 315 = 315 315 + -5x + -1x2 = -315 + 5x + x2 + 315 + -5x + -1x2 Reorder the terms: 315 + -5x + -1x2 = -315 + 315 + 5x + -5x + x2 + -1x2 Combine like terms: -315 + 315 = 0 315 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2 315 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 315 + -5x + -1x2 = 0 + x2 + -1x2 315 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 315 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -315 + 5x + x2 = 0 Move the constant term to the right: Add '315' to each side of the equation. -315 + 5x + 315 + x2 = 0 + 315 Reorder the terms: -315 + 315 + 5x + x2 = 0 + 315 Combine like terms: -315 + 315 = 0 0 + 5x + x2 = 0 + 315 5x + x2 = 0 + 315 Combine like terms: 0 + 315 = 315 5x + x2 = 315 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 315 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 315 + 6.25 Combine like terms: 315 + 6.25 = 321.25 6.25 + 5x + x2 = 321.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 321.25 Calculate the square root of the right side: 17.923448329 Break this problem into two subproblems by setting (x + 2.5) equal to 17.923448329 and -17.923448329.Subproblem 1
x + 2.5 = 17.923448329 Simplifying x + 2.5 = 17.923448329 Reorder the terms: 2.5 + x = 17.923448329 Solving 2.5 + x = 17.923448329 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 17.923448329 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 17.923448329 + -2.5 x = 17.923448329 + -2.5 Combine like terms: 17.923448329 + -2.5 = 15.423448329 x = 15.423448329 Simplifying x = 15.423448329Subproblem 2
x + 2.5 = -17.923448329 Simplifying x + 2.5 = -17.923448329 Reorder the terms: 2.5 + x = -17.923448329 Solving 2.5 + x = -17.923448329 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -17.923448329 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -17.923448329 + -2.5 x = -17.923448329 + -2.5 Combine like terms: -17.923448329 + -2.5 = -20.423448329 x = -20.423448329 Simplifying x = -20.423448329Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.423448329, -20.423448329}
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