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Simplifying 5x2 + 13x + 7 = 0 Reorder the terms: 7 + 13x + 5x2 = 0 Solving 7 + 13x + 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'. 1.4 + 2.6x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 2.6x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + 2.6x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 2.6x + x2 = 0 + -1.4 2.6x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 2.6x + x2 = -1.4 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 = -1.4 + 1.69 Reorder the terms: 1.69 + 2.6x + x2 = -1.4 + 1.69 Combine like terms: -1.4 + 1.69 = 0.29 1.69 + 2.6x + x2 = 0.29 Factor a perfect square on the left side: (x + 1.3)(x + 1.3) = 0.29 Calculate the square root of the right side: 0.538516481 Break this problem into two subproblems by setting (x + 1.3) equal to 0.538516481 and -0.538516481.Subproblem 1
x + 1.3 = 0.538516481 Simplifying x + 1.3 = 0.538516481 Reorder the terms: 1.3 + x = 0.538516481 Solving 1.3 + x = 0.538516481 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 = 0.538516481 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = 0.538516481 + -1.3 x = 0.538516481 + -1.3 Combine like terms: 0.538516481 + -1.3 = -0.761483519 x = -0.761483519 Simplifying x = -0.761483519Subproblem 2
x + 1.3 = -0.538516481 Simplifying x + 1.3 = -0.538516481 Reorder the terms: 1.3 + x = -0.538516481 Solving 1.3 + x = -0.538516481 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 = -0.538516481 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = -0.538516481 + -1.3 x = -0.538516481 + -1.3 Combine like terms: -0.538516481 + -1.3 = -1.838516481 x = -1.838516481 Simplifying x = -1.838516481Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.761483519, -1.838516481}
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