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Simplifying 65 + -5x2 + -4x = 0 Reorder the terms: 65 + -4x + -5x2 = 0 Solving 65 + -4x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -13 + 0.8x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 0.8x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 0.8x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 0.8x + x2 = 0 + 13 0.8x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 0.8x + x2 = 13 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 13 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 13 + 0.16 Combine like terms: 13 + 0.16 = 13.16 0.16 + 0.8x + x2 = 13.16 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 13.16 Calculate the square root of the right side: 3.627671429 Break this problem into two subproblems by setting (x + 0.4) equal to 3.627671429 and -3.627671429.Subproblem 1
x + 0.4 = 3.627671429 Simplifying x + 0.4 = 3.627671429 Reorder the terms: 0.4 + x = 3.627671429 Solving 0.4 + x = 3.627671429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 3.627671429 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 3.627671429 + -0.4 x = 3.627671429 + -0.4 Combine like terms: 3.627671429 + -0.4 = 3.227671429 x = 3.227671429 Simplifying x = 3.227671429Subproblem 2
x + 0.4 = -3.627671429 Simplifying x + 0.4 = -3.627671429 Reorder the terms: 0.4 + x = -3.627671429 Solving 0.4 + x = -3.627671429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -3.627671429 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -3.627671429 + -0.4 x = -3.627671429 + -0.4 Combine like terms: -3.627671429 + -0.4 = -4.027671429 x = -4.027671429 Simplifying x = -4.027671429Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.227671429, -4.027671429}
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