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Simplifying 13x2 + 21x = -5x + 22 Reorder the terms: 21x + 13x2 = -5x + 22 Reorder the terms: 21x + 13x2 = 22 + -5x Solving 21x + 13x2 = 22 + -5x Solving for variable 'x'. Reorder the terms: -22 + 21x + 5x + 13x2 = 22 + -5x + -22 + 5x Combine like terms: 21x + 5x = 26x -22 + 26x + 13x2 = 22 + -5x + -22 + 5x Reorder the terms: -22 + 26x + 13x2 = 22 + -22 + -5x + 5x Combine like terms: 22 + -22 = 0 -22 + 26x + 13x2 = 0 + -5x + 5x -22 + 26x + 13x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -22 + 26x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -1.692307692 + 2x + x2 = 0 Move the constant term to the right: Add '1.692307692' to each side of the equation. -1.692307692 + 2x + 1.692307692 + x2 = 0 + 1.692307692 Reorder the terms: -1.692307692 + 1.692307692 + 2x + x2 = 0 + 1.692307692 Combine like terms: -1.692307692 + 1.692307692 = 0.000000000 0.000000000 + 2x + x2 = 0 + 1.692307692 2x + x2 = 0 + 1.692307692 Combine like terms: 0 + 1.692307692 = 1.692307692 2x + x2 = 1.692307692 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 1.692307692 + 1 Reorder the terms: 1 + 2x + x2 = 1.692307692 + 1 Combine like terms: 1.692307692 + 1 = 2.692307692 1 + 2x + x2 = 2.692307692 Factor a perfect square on the left side: (x + 1)(x + 1) = 2.692307692 Calculate the square root of the right side: 1.640825308 Break this problem into two subproblems by setting (x + 1) equal to 1.640825308 and -1.640825308.Subproblem 1
x + 1 = 1.640825308 Simplifying x + 1 = 1.640825308 Reorder the terms: 1 + x = 1.640825308 Solving 1 + x = 1.640825308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.640825308 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.640825308 + -1 x = 1.640825308 + -1 Combine like terms: 1.640825308 + -1 = 0.640825308 x = 0.640825308 Simplifying x = 0.640825308Subproblem 2
x + 1 = -1.640825308 Simplifying x + 1 = -1.640825308 Reorder the terms: 1 + x = -1.640825308 Solving 1 + x = -1.640825308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.640825308 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.640825308 + -1 x = -1.640825308 + -1 Combine like terms: -1.640825308 + -1 = -2.640825308 x = -2.640825308 Simplifying x = -2.640825308Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.640825308, -2.640825308}
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