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Simplifying 19x + -2x2 + 30 = 0 Reorder the terms: 30 + 19x + -2x2 = 0 Solving 30 + 19x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -15 + -9.5x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -9.5x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -9.5x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -9.5x + x2 = 0 + 15 -9.5x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -9.5x + x2 = 15 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = 15 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = 15 + 22.5625 Combine like terms: 15 + 22.5625 = 37.5625 22.5625 + -9.5x + x2 = 37.5625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 37.5625 Calculate the square root of the right side: 6.128825336 Break this problem into two subproblems by setting (x + -4.75) equal to 6.128825336 and -6.128825336.Subproblem 1
x + -4.75 = 6.128825336 Simplifying x + -4.75 = 6.128825336 Reorder the terms: -4.75 + x = 6.128825336 Solving -4.75 + x = 6.128825336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 6.128825336 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 6.128825336 + 4.75 x = 6.128825336 + 4.75 Combine like terms: 6.128825336 + 4.75 = 10.878825336 x = 10.878825336 Simplifying x = 10.878825336Subproblem 2
x + -4.75 = -6.128825336 Simplifying x + -4.75 = -6.128825336 Reorder the terms: -4.75 + x = -6.128825336 Solving -4.75 + x = -6.128825336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -6.128825336 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -6.128825336 + 4.75 x = -6.128825336 + 4.75 Combine like terms: -6.128825336 + 4.75 = -1.378825336 x = -1.378825336 Simplifying x = -1.378825336Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.878825336, -1.378825336}
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