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Simplifying 21 = 13x + 5x2 Solving 21 = 13x + 5x2 Solving for variable 'x'. Reorder the terms: 21 + -13x + -5x2 = 13x + -13x + 5x2 + -5x2 Combine like terms: 13x + -13x = 0 21 + -13x + -5x2 = 0 + 5x2 + -5x2 21 + -13x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 21 + -13x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -4.2 + 2.6x + x2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + 2.6x + 4.2 + x2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + 2.6x + x2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + 2.6x + x2 = 0 + 4.2 2.6x + x2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 2.6x + x2 = 4.2 The x term is 2.6x. Take half its coefficient (1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. 2.6x + 1.69 + x2 = 4.2 + 1.69 Reorder the terms: 1.69 + 2.6x + x2 = 4.2 + 1.69 Combine like terms: 4.2 + 1.69 = 5.89 1.69 + 2.6x + x2 = 5.89 Factor a perfect square on the left side: (x + 1.3)(x + 1.3) = 5.89 Calculate the square root of the right side: 2.42693222 Break this problem into two subproblems by setting (x + 1.3) equal to 2.42693222 and -2.42693222.Subproblem 1
x + 1.3 = 2.42693222 Simplifying x + 1.3 = 2.42693222 Reorder the terms: 1.3 + x = 2.42693222 Solving 1.3 + x = 2.42693222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = 2.42693222 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = 2.42693222 + -1.3 x = 2.42693222 + -1.3 Combine like terms: 2.42693222 + -1.3 = 1.12693222 x = 1.12693222 Simplifying x = 1.12693222Subproblem 2
x + 1.3 = -2.42693222 Simplifying x + 1.3 = -2.42693222 Reorder the terms: 1.3 + x = -2.42693222 Solving 1.3 + x = -2.42693222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = -2.42693222 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = -2.42693222 + -1.3 x = -2.42693222 + -1.3 Combine like terms: -2.42693222 + -1.3 = -3.72693222 x = -3.72693222 Simplifying x = -3.72693222Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.12693222, -3.72693222}
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