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Simplifying 5x2 + 5 = -13x Reorder the terms: 5 + 5x2 = -13x Solving 5 + 5x2 = -13x Solving for variable 'x'. Reorder the terms: 5 + 13x + 5x2 = -13x + 13x Combine like terms: -13x + 13x = 0 5 + 13x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + 2.6x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 2.6x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 2.6x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2.6x + x2 = 0 + -1 2.6x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2.6x + x2 = -1 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 = -1 + 1.69 Reorder the terms: 1.69 + 2.6x + x2 = -1 + 1.69 Combine like terms: -1 + 1.69 = 0.69 1.69 + 2.6x + x2 = 0.69 Factor a perfect square on the left side: (x + 1.3)(x + 1.3) = 0.69 Calculate the square root of the right side: 0.830662386 Break this problem into two subproblems by setting (x + 1.3) equal to 0.830662386 and -0.830662386.Subproblem 1
x + 1.3 = 0.830662386 Simplifying x + 1.3 = 0.830662386 Reorder the terms: 1.3 + x = 0.830662386 Solving 1.3 + x = 0.830662386 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 = 0.830662386 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = 0.830662386 + -1.3 x = 0.830662386 + -1.3 Combine like terms: 0.830662386 + -1.3 = -0.469337614 x = -0.469337614 Simplifying x = -0.469337614Subproblem 2
x + 1.3 = -0.830662386 Simplifying x + 1.3 = -0.830662386 Reorder the terms: 1.3 + x = -0.830662386 Solving 1.3 + x = -0.830662386 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 = -0.830662386 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = -0.830662386 + -1.3 x = -0.830662386 + -1.3 Combine like terms: -0.830662386 + -1.3 = -2.130662386 x = -2.130662386 Simplifying x = -2.130662386Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.469337614, -2.130662386}
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