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Simplifying 5x2 + -13x + -32 = 0 Reorder the terms: -32 + -13x + 5x2 = 0 Solving -32 + -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'. -6.4 + -2.6x + x2 = 0 Move the constant term to the right: Add '6.4' to each side of the equation. -6.4 + -2.6x + 6.4 + x2 = 0 + 6.4 Reorder the terms: -6.4 + 6.4 + -2.6x + x2 = 0 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 0.0 + -2.6x + x2 = 0 + 6.4 -2.6x + x2 = 0 + 6.4 Combine like terms: 0 + 6.4 = 6.4 -2.6x + x2 = 6.4 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 = 6.4 + 1.69 Reorder the terms: 1.69 + -2.6x + x2 = 6.4 + 1.69 Combine like terms: 6.4 + 1.69 = 8.09 1.69 + -2.6x + x2 = 8.09 Factor a perfect square on the left side: (x + -1.3)(x + -1.3) = 8.09 Calculate the square root of the right side: 2.844292531 Break this problem into two subproblems by setting (x + -1.3) equal to 2.844292531 and -2.844292531.Subproblem 1
x + -1.3 = 2.844292531 Simplifying x + -1.3 = 2.844292531 Reorder the terms: -1.3 + x = 2.844292531 Solving -1.3 + x = 2.844292531 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 = 2.844292531 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = 2.844292531 + 1.3 x = 2.844292531 + 1.3 Combine like terms: 2.844292531 + 1.3 = 4.144292531 x = 4.144292531 Simplifying x = 4.144292531Subproblem 2
x + -1.3 = -2.844292531 Simplifying x + -1.3 = -2.844292531 Reorder the terms: -1.3 + x = -2.844292531 Solving -1.3 + x = -2.844292531 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 = -2.844292531 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = -2.844292531 + 1.3 x = -2.844292531 + 1.3 Combine like terms: -2.844292531 + 1.3 = -1.544292531 x = -1.544292531 Simplifying x = -1.544292531Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.144292531, -1.544292531}
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