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Simplifying 5x2 + 7x + -13 = 24 + -4x Reorder the terms: -13 + 7x + 5x2 = 24 + -4x Solving -13 + 7x + 5x2 = 24 + -4x Solving for variable 'x'. Reorder the terms: -13 + -24 + 7x + 4x + 5x2 = 24 + -4x + -24 + 4x Combine like terms: -13 + -24 = -37 -37 + 7x + 4x + 5x2 = 24 + -4x + -24 + 4x Combine like terms: 7x + 4x = 11x -37 + 11x + 5x2 = 24 + -4x + -24 + 4x Reorder the terms: -37 + 11x + 5x2 = 24 + -24 + -4x + 4x Combine like terms: 24 + -24 = 0 -37 + 11x + 5x2 = 0 + -4x + 4x -37 + 11x + 5x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -37 + 11x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.4 + 2.2x + x2 = 0 Move the constant term to the right: Add '7.4' to each side of the equation. -7.4 + 2.2x + 7.4 + x2 = 0 + 7.4 Reorder the terms: -7.4 + 7.4 + 2.2x + x2 = 0 + 7.4 Combine like terms: -7.4 + 7.4 = 0.0 0.0 + 2.2x + x2 = 0 + 7.4 2.2x + x2 = 0 + 7.4 Combine like terms: 0 + 7.4 = 7.4 2.2x + x2 = 7.4 The x term is 2.2x. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2x + 1.21 + x2 = 7.4 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = 7.4 + 1.21 Combine like terms: 7.4 + 1.21 = 8.61 1.21 + 2.2x + x2 = 8.61 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 8.61 Calculate the square root of the right side: 2.93428015 Break this problem into two subproblems by setting (x + 1.1) equal to 2.93428015 and -2.93428015.Subproblem 1
x + 1.1 = 2.93428015 Simplifying x + 1.1 = 2.93428015 Reorder the terms: 1.1 + x = 2.93428015 Solving 1.1 + x = 2.93428015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = 2.93428015 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 2.93428015 + -1.1 x = 2.93428015 + -1.1 Combine like terms: 2.93428015 + -1.1 = 1.83428015 x = 1.83428015 Simplifying x = 1.83428015Subproblem 2
x + 1.1 = -2.93428015 Simplifying x + 1.1 = -2.93428015 Reorder the terms: 1.1 + x = -2.93428015 Solving 1.1 + x = -2.93428015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = -2.93428015 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -2.93428015 + -1.1 x = -2.93428015 + -1.1 Combine like terms: -2.93428015 + -1.1 = -4.03428015 x = -4.03428015 Simplifying x = -4.03428015Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.83428015, -4.03428015}
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