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Simplifying -2x2 + -20x = -23 Reorder the terms: -20x + -2x2 = -23 Solving -20x + -2x2 = -23 Solving for variable 'x'. Reorder the terms: 23 + -20x + -2x2 = -23 + 23 Combine like terms: -23 + 23 = 0 23 + -20x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -11.5 + 10x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + 10x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + 10x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + 10x + x2 = 0 + 11.5 10x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 10x + x2 = 11.5 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 = 11.5 + 25 Reorder the terms: 25 + 10x + x2 = 11.5 + 25 Combine like terms: 11.5 + 25 = 36.5 25 + 10x + x2 = 36.5 Factor a perfect square on the left side: (x + 5)(x + 5) = 36.5 Calculate the square root of the right side: 6.041522987 Break this problem into two subproblems by setting (x + 5) equal to 6.041522987 and -6.041522987.Subproblem 1
x + 5 = 6.041522987 Simplifying x + 5 = 6.041522987 Reorder the terms: 5 + x = 6.041522987 Solving 5 + x = 6.041522987 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 = 6.041522987 + -5 Combine like terms: 5 + -5 = 0 0 + x = 6.041522987 + -5 x = 6.041522987 + -5 Combine like terms: 6.041522987 + -5 = 1.041522987 x = 1.041522987 Simplifying x = 1.041522987Subproblem 2
x + 5 = -6.041522987 Simplifying x + 5 = -6.041522987 Reorder the terms: 5 + x = -6.041522987 Solving 5 + x = -6.041522987 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 = -6.041522987 + -5 Combine like terms: 5 + -5 = 0 0 + x = -6.041522987 + -5 x = -6.041522987 + -5 Combine like terms: -6.041522987 + -5 = -11.041522987 x = -11.041522987 Simplifying x = -11.041522987Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.041522987, -11.041522987}
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