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Simplifying -0.03x2 + 0.3x + 15 = 0 Reorder the terms: 15 + 0.3x + -0.03x2 = 0 Solving 15 + 0.3x + -0.03x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.03 the coefficient of the squared term: Divide each side by '-0.03'. -500 + -10x + x2 = 0 Move the constant term to the right: Add '500' to each side of the equation. -500 + -10x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + -10x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + -10x + x2 = 0 + 500 -10x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 -10x + x2 = 500 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 500 + 25 Reorder the terms: 25 + -10x + x2 = 500 + 25 Combine like terms: 500 + 25 = 525 25 + -10x + x2 = 525 Factor a perfect square on the left side: (x + -5)(x + -5) = 525 Calculate the square root of the right side: 22.912878475 Break this problem into two subproblems by setting (x + -5) equal to 22.912878475 and -22.912878475.Subproblem 1
x + -5 = 22.912878475 Simplifying x + -5 = 22.912878475 Reorder the terms: -5 + x = 22.912878475 Solving -5 + x = 22.912878475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 22.912878475 + 5 Combine like terms: -5 + 5 = 0 0 + x = 22.912878475 + 5 x = 22.912878475 + 5 Combine like terms: 22.912878475 + 5 = 27.912878475 x = 27.912878475 Simplifying x = 27.912878475Subproblem 2
x + -5 = -22.912878475 Simplifying x + -5 = -22.912878475 Reorder the terms: -5 + x = -22.912878475 Solving -5 + x = -22.912878475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -22.912878475 + 5 Combine like terms: -5 + 5 = 0 0 + x = -22.912878475 + 5 x = -22.912878475 + 5 Combine like terms: -22.912878475 + 5 = -17.912878475 x = -17.912878475 Simplifying x = -17.912878475Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.912878475, -17.912878475}
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